The general consensus up until now is, roughly:
Homo Erectus: 1 million B.C. to about 500,000 B.C.
Homo Neanderthalensis and Homo Sapiens split off from common ancestor: 500,000 B.C.
Homo Sapiens dominate Africa until about 70,000 B.C. when they spread into Europe, Middle East, and Asia.
Neanderthals dominate Europe, Middle East, and Asia, until 70,000 B.C. when Homo Sapiens return out of Africa.
There are a few other variations of humans in the 300KYA to 70KYA period, including:
Denisovans (found in Siberia and other places), the "hobbits" found in Indonesia.
It's possible and likely that around 100KYA, there were several species of humans cohabiting the earth, including modern humans (H. sapiens), Neanderthals, Denisovans, a few remaining H. Erectus, the hobbits, and some mixtures of the above.
Each discovery sheds new light and sometimes, as with this possible modern human skull, shatters old theories about the timeline.
It's fascinating to think that at one time in the not-too-distant past, there were multiple species of humans in existence, of which only one survived, though most non-African humans today carry 2-4% Neanderthal genes, so in a sense, some traits of the Neanderthals survived. We are the Neanderthals.
It's time we stopped using the term "Neanderthal" as an insult. They were possibly as smart as modern humans, had larger brains, had tools, ritual burial, weapons technologies, and art work. Their anatomical structure indicates that likely they had language. It's possible that they were gentler than H. Sapiens which would explain how they got gobbled up and made extinct, despite their vast strength (Neanderthals bone structure and muscle attachments indicate that they were many times stronger than modern humans.)