  This survey is concerned with the power of random information for
approximation in the (deterministic) worst-case setting, with special emphasis
on information consisting of functionals selected independently and identically
distributed (iid) at random on a class of admissible information functionals.
We present a general result based on a weighted least squares method and derive
consequences for special cases. Improvements are available if the information
is ``Gaussian'' or if we consider iid function values for Sobolev spaces. We
include open questions to guide future research on the power of random
information in the context of information-based complexity.
