OK, lemme see if I can explain this properly. If someone identifies any errors then they are welcome to correct me.
The prevailing view is that Homo erectus emerged in Africa roughly 2 million years ago. Then, Homo erectus was the first hominid known to have dispersed out of Africa into the Levant and Southeast Asia, roughly 1.8 million years ago. That's the easy part, then things get dicey.
Although not universally accepted, the prevailing view now is that Homo erectus in Africa evolved into Homo antecessor by roughly 900,000 years ago, and that this was the last common ancestor of Neanderthals and modern humans. By roughly 800,000 years ago, Homo antecessor spread into southwestern Europe (i.e., Spain).
By around 500,000 years ago this population then evolved into Homo heidelbergensis (who was previously thought the last common ancestor of Neanderthals and humans, before the discovered of H. antecessor). There's some dispute about the proper classification of H. heidelbergensis. Many paleoanthropologists regard H. heidelbergensis as an intermediate "chronospecies" - that is, a species that has altered so much over the passage of time that if members of the species had lived at the same time as members of the same species hundreds of thousands of years beforehand they would be regarded as different species, although technically they are the same species. (This might be confusing. If you want, I can try to explain the concept a bit more.)
In any event, by about 200,000 years ago H. heidelbergensis had evolved into H. neanderthalensis. The Neanderthals then spread throughout Europe from west to east, and later into the Levant, when an Ice Age pushed the H. sapiens out of the Levant back into Africa. So the arrow of speciation is as follows:
Homo erectus -> Homo antecessor-> Homo heidelbergensis -> Homo neanderthalensis.
Meanwhile, back in Africa, Homo antecessor continued evolving until early Homo sapiens emerged as two subspecies roughly 200,000 years ago. There is some controversy as to the correct relationship between H. sapiens and a set of fossils previously known as Homo rhodesiensis, now thought to date roughly 300,000 years ago. Some paleoarchaeologists regard this as an intermediate species, others as a chronospecies perhaps in continuity with H. heidelbergensis (this was the pre-H. antecessor view), and others as an archaic Homo sapiens.
In any event, one of the known H. sapiens subspecies went extinct around 150,000 years ago and the other became us. According to mtDNA studies, the most recent common ancestor of all humans alive today lived in Africa 171,500 years ago (give or take a bit). The currently prevailing view is that this Anatomically Modern Homo Sapiens (AMHS) migrated out of Africa roughly 100,000 years ago and replaced other hominid populations throughout Asia and Europe.
So, the arrow of speciation of AMHS modern humans would be:
Homo erectus -> Homo antecessor-> "Archaic" Homo sapiens (arguably Homo rhodesiensis or Homo heidelbergensis) -> Homo sapiens sapiens