An introduction to b-minimality
  We give a survey with some explanations but no proofs of the new notion of b-minimality by the author and F. Loeser [b-minimality, J. Math. Log., 7 no. 2 (2007) 195--227, math.LO/0610183]. We compare this notion with other notions like o-minimality, C-minimality, p-minimality, and so on. 
R. Cluckers