Comparison of Modern Human and Neanderthal skulls from the Cleveland Museum of Natural History.
Photo by hairymuseummatt and DrMikeBaxter.Here’s the timeline presented by the authors. Six million years ago (mya) our ancestors split from chimps. I’m obviously skipping some intermediate steps, but about 1.8 mya, Homo erectus dispersed from Africa across the world. However, a group of H. erectus that remained in Africa eventually evolved into H. heidelbergensis. About 500 kya, one group of H. heidelbergensis spread through Europe and evolved into Neanderthals. A second group of H. heidelbergensis stayed in Africa and, between 100-200 kya, evolved into modern humans. Some of these humans subsequently spread throughout the globe in a third dispersion wave.
Dediu D, & Levinson SC (2013). On the antiquity of language: the reinterpretation of Neandertal linguistic capacities and its consequences. Frontiers in psychology, 4 PMID: 23847571