I'm a fan of shows and movies that depict the colonization of space: Firefly, The Expanse, 2001 a Space Odyssey, etc. I'm a true believer: Unless we manage to destroy ourselves first, the Human Race will eventually have extensive colonies in space.
Space colonies are a lot different than colonies in the new world, India, China, Africa, etc 4 centuries ago, or by various cultures around the Mediterranean and other places 2000 years ago. For starters, there were already people living in most of these places--they had air to breathe, soil to plant crops in, etc. This is not true in space. We will either have to bring these things with us or make them there. Colonization opened people up to new diseases and other problems in the old days; that will also be true of space: Radiation poisoning, lack of gravity, price of air and water, etc. My dad, who worked for decades designing satellites, is skeptical that we will ever be able to overcome these, but I think we will. But it will be hard and it will take much longer than people like Elon Musk imagine.
The first nasty problem is the difficulty in getting people and goods from Earth's surface into space. This is very hard, but there's nothing completely intractable about it. Chemical rockets can do it, but at great expense. SpaceX, to their credit, have moved the needle considerably. Several science fiction writers have proposed some sort of fusion rocket, which can be profoundly more efficient. This will require a breakthrough to achieve, although it's superficially plausible. Several SF stories, Such as The Expanse and Firefly have followed this route. Breakthroughs, unlike more straightforward engineering, are difficult to predict, but I understand enough of the physics to be pretty confident that the breakthrough will happen, most likely in the next half century or so.
The next problem is gravity. It turns out that humans need some gravity to be healthy, although we can tolerate its absence for a while. Many SciFi stories imply or require some sort of artificial gravity--Star Trek and Firefly are two notable cases, although little detail is given. Gravity Plating, as suggested by Star Trek, will require a pretty big breakthrough--comparable to the Warp Drive of that same milieu. It's plausible that they are related--In Einsteinian General Relativity, gravity is an artifact of the warping space by large masses. There may be other ways to warp space, ways which allow faster than light travel or gravity plating, but these are completely outside our present understanding of physics.
The Expanse does away with artificial gravity: they make it the old fashioned way, by accelerating. In space ships, they are designed so that thrust is aligned with the axis of the ship, and any acceleration or deceleration gives the occupants a pretty realistic impression of gravity. In the stories, which are mostly about warfare in space, accelerations well over 1 G are commonplace, but I think the vast majority of ships will remain comfortably 1 G or less the vast majority of the time. The second way, of course, is to spin things--centrifugal space ships. Several of the space colonies in the stories are asteroids, which have been spun up to create artificial gravity and hollowed out. A little engineering shows that this is implausible. A 1 G force on a several mile long cable exceeds the tensile strength of most rocky-based materials, including iron. Centrifugal colonies will be largely artificial and their diameter will be only a few miles at most. They may be very long--more like O'neill cylinders and less like those envisioned by von Braun and Chesley Bonnestal. They might be made from material harvested from asteroids like Ceres, but they will not simply be those asteroids.
The third difficult, but not intractable problem, is radiation. All manned space missions so far have been one of two things: very short or, beneath the van Allen Radiation belts, which protect us from a lot of radiation. A colony on the moon, Mars, or in a space station or elsewhere, will need considerable radiation shielding. The simplest way to do this today is using many feet of shielding. Heavy metals like Lead are the most effective by thickness, but a much thicker layer of dirt or water is much more effective. I'm think that most space habitations, including those in centrifugal stations, will be protected by ten meters or more of whatever material is most convenient. Digging deep underground will be the simplest way to provide this.
Water is relatively common in space, but it will be a limited resource for most colonies. Air is a little more problematic, but not really. We can breathe any non-poisonous gas that contains enough Oxygen and CO2. On earth, Nitrogen is most convenient and likely will be in space too, but we're far from limited. Oxygen can be made from water and other things by Electrolysis and is a byproduct of photosynthesis.
We will need plants growing in space to feed ourselves. Simply dedicating surface area to plants is not particularly efficient: The most solar-efficient plants are well under 1%, where present photovoltaics can easily do 15%. Put photovoltaics on all possible surfaces and grow plants underground under efficient electric lighting. The photovoltaics are much more tolerant of radiation than plants are are relatively easy to replace, and to manufacture from materials that we already know are on The Moon and Mars.
Presuming we don't drive ourselves extinct first (and Elon Musk and Donald Trump are presently the leading individuals working towards making us extinct) I think we will have permanent colonies in space by 2050 or so, and self-sufficient colonies some time after 2100. The sorts of populations on Mars and Ceres envisioned in The Expanse are unlikely to occur until there is a major breakthrough, such as the Expanse's Epstein Drive, but I'd think that by 2200 there will be tens of thousands of people living, breeding and dying entirely in space. Not the millions portrayed by the Expanse.