While Elon Musk recently revealed plans for his Interplanetary Transport System and his ambitions to colonize Mars, there are other ways for humanity to travel the cosmos.
One of those is the idea of Von Neumann Machines, which are self-replicating autonomous probes that would head off into space and seek out distant planets. They would then use the resources of the planet to replicate themselves, then head off to explore somewhere else. They would continue to do this until there would be millions of them exploring the cosmos.
In this TED Educational video by Dr. Roey Tzezana it's explained exactly how these machines, named after mathematician John von Neumann, would help humanity colonize the galaxy. As the video notes there are around 300 billion stars in our galaxy alone, to see if any of them had planets orbiting that might be of interest would take a very long time indeed with manned space flight.
By sending machines there it would not only be done quicker, but they could also send back data and assess whether it was worth sending humans there.
Von Neumann even designed, on paper, these self-replicating machines and theoretically it's possible to create them. The science and technology isn't there quite yet, because we would need advanced artificial intelligence and the ability to artificially grow biological organisms.
But one day, we might create them. Or perhaps another civilization has already created them—they just haven't arrived on earth. Yet.