We give a short introduction to IBC and present some basic definitions and a few results. The general question is: How many function values (or values of other functionals) of

*f*do we need to compute*S*(*f*) up to an error ϵ? Here*S*(*f*) could be the integral or the maximum of*f*. In particular we study the questions: Which problems are tractable? When do we have the curse of dimension and how can we avoid the curse?