In the ancient times astrology was a recurring topic for all cultures, be it having Mars rising as you were born to the Romans making you a warrior, the year of the Dragon being auspicious for the Chinese or your future rise or fall as a Babylonian king. It was almost common sense that those elevated in the astral realms that we today call planets were living gods, who acted and reached to humans in certain occasions of their cycles. Today, and for the last ≈ 500 years, astrology became a forgotten about "science", and even calling it science is laughing matter for any person who declares themselves as logical. Though, happily most of it's teachings were maintained by small groups who could see it's efficacy through time, transmitting the knowledge from one to another as time went on.
Ancient Astrology
The Babylonians and very ancient civilizations, mostly used astrology in an very different manner compared to how we commonly use today. While today it's mostly seem as something natal and that determines who you are and were you'll go, in those times it was mostly seem as signs from the heavens which defined the fate of the whole nation. It's start as a natal focused science was mostly developed by the greeks. It was then that it got most of the aspects we can recognize today, such as the aascendant, the houses, the mathematical aspects and meanings. Astrology in the pre-christianity time is pretty characteristic by the understanding of the planets as actual gods. Those assumptions, although absurd for the modern mind, were true in a manner. The planets each represent cardinal aspects of reality, and given that their dance is the time passage of existence itself, the understanding of the planets as the polytheistic gods, or at least as their influence, was an extremely rational conclusion to make.
The pre-modern astrology is also characterized by how "black and white" it is in comparison to how it's today. Saturn and Mars were considered "the Malefic planets", calling them that today would make you get stares at a new age store. The 2 malefics could be considered beneficial to the individual depending on their position and circumstance, but it still would be considered bad for other people. In example, someone with a perfect Saturn(Born during the day, with Saturn on the Tenth house, before the Sun rises) would have lots of victories involving authority, terrain and nobility. But those victories would mean loss for the people around who were also aiming at it. Someone born with a perfect Mars (Born during the night, Mars rising before the Sun, Mars in the ascendant or the tenth house) would win many battles and have lots of victories in war,which is good for the individual, but also meaning the disgracing and destruction of other people. The 2 malefics would always manifest as evil in somewhere, having them in a lucky place would only make it so you're not the one in their aim. As only the visible planets in the sky were used, the rulership system was also made of only 7 planets:
Sun:The most powerful and representative of the soul/consciousness of the individual. The greek god Apollo, the roman god Helios and later in western astrology, defined as Jesus Christ. If a planet rises after the Sun, it was considered a feminized planet. Which made it's effects slower but more graceful, while if a planet rised before the Sun, it was considered more masculinized, which made it's effects both faster and also more reckless. Is considered the ruler of the day, and thus powerful in every diurnal chart.
Moon:The subconscious and unconscious of the individual, the emotions, the early life, the mom and the home. Is considered the ruler of the night, thus more powerful in every nocturnal chart. Creates good writers when on the ascendant.
Mercury:The planet of communication and low distance mental and physical travel, know by it's quickness, Also rules commerce and thievery. Natally controls how the individual expresses and communicates himself. Brings luck to public life if risen before the Sun, brings luck to intimate life if risen after the Sun. Hermes and Mercury.
Venus:The planet of femininity and pleasure, known by the Babylonians as Ishtar, the queen of heaven, and later as Afrodite by the greeks. "The lesser benefic", is more powerful in nocturnal charts. As a feminine planet it also operates better if it rises after the Sun. Makes one artistic if on the tenth house or the ascendant.
Mars:The planet of masculinity and war, known by the Greeks as Aries. "The lesser malefic". Brings enemies, or makes the person reckless and violent if born during the day. Makes the person powerful and victorious if born during the night. When in the ascendant or the tenth house, creates an athlete or an warrior.
Jupiter:The planet of Long distance mental and physical travel. Zeus for the Greeks, considered "The greater benefic". Brings luck, expansion, optmism, glory, gifts and excess. By ruling long distance mental travel(in modern terms, Deep and higher study) , it also brings great wisdom and knowledge. When in the ascendant makes one charismatic and optimistic, common in nobility. Most powerful during the day.
Saturn:The planet of authority, limitations and public life. Chronos for the greeks, considered "The greater malefic" Also later associated with Satan. Brings limits, punishing and misery. powerful when in a Diurnal chart above the horizon, makes the individual victorious in his endeavors, specially if terrains or authority is involved.
Above is the traditional rulership system, as a small difference from today, they were not called "Ruler" of a certain sign, but "Lord". Mars and Venus both oppose each other 2 times, the first time at Aries and Libra, Mars ruling War, Violence and Victory(Aries), while Venus ruling Peace, Fairness and Relationships(Libra). The second time happens right after Aries, with Taurus and Scorpio. Mars ruling Power, Sex and Influence(Scorpio) while Venus rules Pleasures, Abundance and Security(Taurus). Saturn opposes both the Sun and the Moon, as the greater malefic. Jupiter and Mercury also double opposition each other 2 times, representing the difference of lower day to day thinking (Mercury) and the higher thinking and faith(Jupiter). First time at Gemini and Sagittarius, with Mercury ruling short distance travel and logic(Gemini), and Jupiter ruling long distance travel, faith and ideals. The second time happening at Virgo and Pisces, with Mercury ruling the day to day work-life, health and details(Virgo), while Jupiter rules dreams, transcendence and the whole(pisces).
One tradition that passed on to modern astrology without any change, is that planets get stronger when they're in their signs(i.e Jupiter in Sagittarius), or signs that sinergize with their function(i.e Venus in pisces), and also the opposite, they get weaker or distorted if the sign is opposite to their rule(i.e Sun in Aquarius). During the ancient times, the act of just divination by looking at the current stars also became common, which today is known as Horary astrology. Horary astrology became very popular with the passing of time, as it was way more practical to the common use, for not everyone knew their exact time of birth.
Modern Astrology
The finding of the 3 new planets, together with the rapid changing of society values, reshaped astrological thinking a lot in the last two centuries compared to how it was before. Saturn and Mars were both no longer considered that bad, with the punishment of Saturn being slowly considered less of a Satanic 5d influence in your life, and more of just a "teacher" of some sorts. The area also became slowly way less deterministic and more tendency focused, it basically started trying to larp as a modern science. Lots of progress in understanding the planets were made in this era though, the understanding of the planets as not more only the effects they caused, but also the archetypes which they represented in the metaphysical and the mind. It wasn't anymore "Planet X causes this on my life", it became more "Planet X represents this part of me which manifests itself as X on my life".
During modern astrology, not only the rulerships were changed, but also, the concept of house-sign correlations was created. "Aries=1st house, Taurus = 2nd(...)" is an modern astrology creation. Talking informally, modern astro really buffed Aquarius, making it go from a nasty Saturn-ruled fractured sun collectivist hive mind sign, to the "Innovation and individuality" now that Uranus is attributed to it. Pisces got nerfed too, from Jupiter which ruled transcendence and higher thinking, to Neptune, which rules fugging transcendence but also escapism and suicide. As a pisces, i really think the devs need to go back in this; Scorpio didn't change much though.
Now going back to seriousness, the planets which come after saturn are odd ones, as they represent things even bigger than saturn. Saturn represents reality itself, as it rules the passage of time and the space, the structure of reality itself. And coming right after it, we find Uranus, the planet of pure Energy, of infinite ideas and power. Uranus' influence, along with all other's which come after it(Neptune and Pluto), is limited by Saturn of entering material reality, as they represent things way bigger. but still, whenever a natal conjunction happens involving those planets, their effects come in full at the individual. Uranus, being all energy and ideas, manifests itself as individuality and creativity in the person. It makes the person different from the "normal"(Saturn rules societal structures too, after all) in general, it creates resistance towards the common, and willfullness to bring new things.
While Uranus manifests it's otherworldly infinite influence by innovation inside the saturnine structure, it gets way more foggy when we go to Neptune. Neptune is the planet of Spirituality, Illusions and dreams, Meaning it basically rules over everything that can be imagined, everything outside of the material. This energy can manifest in the individual in many forms, though the 2 most common in today's world are: Escapism(as dealing with the material day to day reality is not fulfilling for the individual) or utopian ideologies(Very likely if the person has aquarius tendencies together with the strong Neptune). It is a dangerous planet, leading even to the most direct meaning of "Self-undoing" which pisces rules in some cases, but that energy can be greatly manifested if directed towards creative endeavors or actual spirituality.
Pluto is an even stranger one, ruling the universal and eternal concept and energy of transformation, thus ruling the cycle of death and reencarnation, the old and the new, the eternal changing. It manifests itself in people in very different manners, harmonic aspects can make it so that the person is very relaxed with changes in their life, or that the changes in themselves are good for the person. Stressful aspects create tension against change though, which turns into compulsion, evolving sometimes into obsession. People with a very strong Pluto in themselves will feel the need to manifest that transformation somewhere in their lives, inside or outside, depending on the rest of their chart. Can be brutal if taken to extremes.
Another great change was the abandoning of the Whole signs system, which was the house system used by the ancients. The system revolved into the house being the whole sign, i.e even if you were born with asc in 29' Libra, the Entire sign of Libra would be your first house, the entire sign of Scorpio your second, etc. But with the coming of Placidus and others, having more more precise house calculations, the whole signs system was slowly overshadowed. Some astrologers still use whole signs, I've personally found that both seem to work more or less. I believe that the house cusps, (mainly the MC and the ASC) go a bit beyond what is just shown on the chart, and that's what causes both systems working without too much contradiction. If Placidus, Koch or whatever doesn't fit, go whole signs, even more if the time of birth is not totally exact, whole signs is specially a life saver in those situations.
Conclusion
If you want some fun and also some practical stuff, study ancient astrology. if you want actual deep metaphysical understanding, go modern. If you just want to be good at astrology, study both and integrate their techniques. Even though something can be "Outdated" or from diverging systems, it still works, as everything in reality is eternally mirrored from itself. Which one works? Babylonian? Greek? Medieval? Modern? The answer is all of them, if you're good enough.