  This is a survey of recent results on central and non-central limit theorems
for quadratic functionals of stationary processes. The underlying processes are
Gaussian, linear or L\'evy-driven linear processes with memory, and are defined
either in discrete or continuous time. We focus on limit theorems for Toeplitz
and tapered Toeplitz type quadratic functionals of stationary processes with
applications in parametric and nonparametric statistical estimation theory. We
discuss questions concerning Toeplitz matrices and operators, Fej\'er-type
singular integrals, and L\'evy-It\^o-type and Stratonovich-type multiple
stochastic integrals. These are the main tools for obtaining limit theorems.
