  This survey addresses sampling discretization and its connections with other
areas of mathematics. The survey concentrates on sampling discretization of
norms of elements of finite-dimensional subspaces. We present here known
results on sampling discretization of both integral norms and the uniform norm
beginning with classical results and ending with very recent achievements. We
also show how sampling discretization connects to spectral properties and
operator norms of submatrices, embedding of finite-dimensional subspaces,
moments of marginals of high-dimensional distributions, and learning theory.
Along with the corresponding results, important techniques for proving those
results are discussed as well.

Functional Analysis