  The Performance Estimation Problem (PEP) approach consists in computing
worst-case performance bounds on optimization algorithms by solving an
optimization problem: one maximizes an error criterion over all initial
conditions allowed and all functions in a given class of interest. The maximal
value is then a worst-case bound, and the maximizer provides an example
reaching that worst case. This approach was introduced for optimization
algorithms but could in principle be applied to many other contexts involving
worst-case bounds. The key challenge is the representation of
infinite-dimensional objects involved in these optimization problems such as
functions, and complex or non-convex objects as linear operators and their
powers, networks in decentralized optimization etc. This challenge can be
resolved by interpolation constraints, which allow representing the effect of
these objects on vectors of interest, rather than the whole object, leading to
tractable finite dimensional problems. We review several recent interpolation
results and their implications in obtaining of worst-case bounds via PEP.
