In the first part of my talk I will introduce the category of Chow motives (discovered by Alexander Grothendieck some 40 years ago). In particular I will define Rost nilpotence and explain why this is an important feature of smooth and proper schemes. In the second part of the talk I will present some recent results on the question whether Rost nilpotence is true for all smooth and proper schemes (over a field) or not.