Contents  
1 Introduction  
2 Birth of a conjecture  
3 Index maps in K-theory: the contribution of Kasparov  
4 Towards the official version of the conjecture  
5 Full and reduced C*-algebras  
6 Banach algebraic methods  
7 The Baum-Connes conjecture for groupoids  
8 The coarse Baum-Connes conjecture (CBC)  
9 Outreach of the Baum-Connes conjecture  