  The aim of this work is to give an overview of the recent developments in the
area of statistical inference for parabolic stochastic partial differential
equations. Significant part of the paper is devoted to the spectral approach,
which is the most studied sampling scheme under which the observations are done
in the Fourier space over some finite time interval. We also discuss into
details the practically important case of discrete sampling of the solution.
Other relevant methodologies and some open problems are briefly discussed over
the course of the manuscript.
