  This is a survey of the book arXiv:0810.5645 with Yinan Song. Let X be a
Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers
DT^a(t) which count stable sheaves with Chern character a on X, with respect to
a Gieseker stability condition t. They are defined only for Chern characters a
for which there are no strictly semistable sheaves on X. They have the good
property that they are unchanged under deformations of X. Their behaviour under
change of stability condition t was not understood until now.
  We discuss "generalized Donaldson-Thomas invariants" \bar{DT}^a(t). These are
rational numbers, defined for all Chern characters a, and are equal to DT^a(t)
if there are no strictly semistable sheaves in class a. They are
deformation-invariant, and have a known transformation law under change of
stability condition. We conjecture they can be written in terms of integral
"BPS invariants" \hat{DT}^a(t) when the stability condition t is "generic".
  We extend the theory to abelian categories of representations of a quiver
with relations coming from a superpotential, and connect our ideas with
Szendroi's "noncommutative Donaldson-Thomas invariants" and work by Reineke and
others. There is significant overlap between arXiv:0810.5645 and the
independent paper arXiv:0811.2435 by Kontsevich and Soibelman.
