A 2015 review paper on archaic human introgression by Fernando Racimo and coworkers has a wonderfully succinct summary of the modern human origins debate:
The relationship between modern humans and other, now extinct, archaic hominin groups has been a subject of controversy since the 1970s. Two competing hypotheses were originally proposed: the multiregional model posited that modern humans evolved in parallel throughout Africa and Eurasia from different archaic groups while exchanging migrants, whereas the out-of-Africa model proposed that all present-day humans had a recent origin in the African continent, from which they expanded across the world. However, over the past 30 years, these two hypotheses were increasingly seen as an over-simplification.
The only quibble I have is that the debate began closer to the 1870s than the 1970s!