The highly redshifted hyperfine line of neutral hydrogen presents a powerful means of tracking Cosmic Dawn, with potential to be a unique probe into the Dark Ages. There are significant ground-based efforts underway to detect both the global sky-averaged signature and the power spectrum from the Epoch of Reionization (z ~ 10). However, at higher redshifts, ground-based efforts will increasingly have to contend with the phase fluctuations and opacity from the Earth's ionosphere, necessitating a transition to space. I summarize avenues and prospects for space-based probes of Cosmic Dawn and the Dark Ages in the next decade.