  In this self-contained chapter, we revisit a fundamental problem of
multivariate statistics: estimating covariance matrices from finitely many
independent samples. Based on massive Multiple-Input Multiple-Output (MIMO)
systems we illustrate the necessity of leveraging structure and considering
quantization of samples when estimating covariance matrices in practice. We
then provide a selective survey of theoretical advances of the last decade
focusing on the estimation of structured covariance matrices. This review is
spiced up by some yet unpublished insights on how to benefit from combined
structural constraints. Finally, we summarize the findings of our recently
published preprint "Covariance estimation under one-bit quantization" to show
how guaranteed covariance estimation is possible even under coarse quantization
of the samples.
