Tracking cells through Embryo Development ?

[Widdekind]

Once a fertilized egg begins dividing, at what point do the new (daughter) cells start specializing ? For example, do all nerve cells originate, from one of the 4 cells in the embryo, after 2 divisions ? By what means, do identical cells "sort out", the "who does what" ? What is the "ok, my line will produce the nervous system", "hey, ok, I'll do the digestive track", ..., etc., "sorting out" procedure, amongst developing embryo cells ??

 

(Thanks in advance, for any answers, to my questions.)