A multivariate random process or field is called operator self-similar (o.s.s.) when its law satisfies an (operator) scaling relation according to a matrix Hurst parameter. In particular, the so-named operator fractional Brownian motion (OFBM) is the natural multivariate extension of the univariate fractional Brownian motion. The construction of inferential methods for o.s.s. processes turns out to be rather challenging due to the presence of mixed power laws. In this talk, we will provide a broad description of the problem of modeling operator self-similarity and illustrate how operator scaling laws naturally appear in physical applications. The discussion will be centered on the wavelet estimator for OFBMs recently put forward in Abry and Didier (2015).