All people today are classified as Homo sapiens.  Our species of humans first began to evolve nearly 200,000 years ago in association with technologies not unlike those of the early Neandertals.  It is now clear that early Homo sapiens, or modern humans, did not come after the Neandertals but were their contemporaries.  However, it is likely that both modern humans and Neandertals descended from Homo heidelbergensis.
Compared to the Neandertals and other late archaic humans, modern humans generally have more delicate skeletons.  Their skulls are more rounded and their brow ridges generally protrude much less.  They rarely have the occipital buns found on the back of Neandertal skulls.  They also have relatively high foreheads, smaller faces, and pointed chins.