How did humans spread around the world?

We know that all human beings (Homo sapiens sapiens) can trace their origins back to Africa. Sometime between 100 and 200 thousand years ago (ka) the first of these modern humans migrated out of Africa and spread across the rest of the globe.
One line of evidence for this is that the further you go from sub-Saharan Africa, the more similar people are genetically.

Think about this way: let’s say there are ten different people living in Africa. One of them leaves. Over the next 100 ka, his descendants settle throughout Asia, but they all still share the common ancestor that left Africa. The descendants of the nine people who remained in Africa have no such commonality. Their shared ancestor dates from the evolution of the human species far earlier. Therefore, the people living in Africa today are far more diverse genetically than any of the groups living elsewhere in the world.

So far so good. What isn’t clear is whether the dispersal from Africa occurred as a single event or multiple events at different times in history. And what route did those groups of people use as they traveled around the world? Hugo Reyes-Centeno of Eberhard Karls University of Tübingen and his colleagues used both genetics and cranial features to compare four possibilities: a single dispersal with a northern route, a single dispersal with a southern route, multiple dispersals using both routes, and multiple dispersals using both routes, but where groups of people became stranded and thus genetically isolated along the way.

They conclude that the most likely scenario is the last one. Around 130 ka, humans began traveling across Southern Asia. A separate diaspora occurred about 50 ka taking humans into Europe.

Reyes-Centeno, H., Ghirotto, S., Detroit, F., Grimaud-Herve, D., Barbujani, G., & Harvati, K. (2014). Genomic and cranial phenotype data support multiple modern human dispersals from Africa and a southern route into Asia Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1323666111.