And these breakthroughs are by no means guaranteed. Remember, we still don’t have flying skateboards, despite all the technological progress since Back to the Future came out.
What’s stopping us is physics itself, not lack of sufficiently complex technology.
In the far enough future, and assuming we escape a technological collapse due to climate change or world war, something like a large base housing hundreds of people at a time seems possible. It could be built autonomously by reasonably intelligent robots, which isn't that much of a stretch from the tech we're converging on today.
But a true colony, with long term residents having and raising children, is essentially a fantasy at this point.
2) Ability to recreate Earth-like conditions including gravity, atmosphere, sunshine, farming and raising livestock on a massive scale (hundreds of square kilometers) on Mars.
3) Ability to create adequate conditions for the transport phase.
4) Ability to justify the investment (most issues on earth solved, remember opportunity cost).