A survey on moments of a class of error terms

This is a survey article on the moments of a class of error terms in analytic number theory. We begin by reviewing the moments of the Dirichlet divisor problem, and then review the hybrid moments of error terms in the divisor problems. We give two new results on the joint distribution of sign changes of ${\mathrm{\Delta }}_2(x)$ and ${\mathrm{\Delta }}_3(x)\mathrm{.}$ In the last section, we present some conjectures on the moment results in the well-known Selberg class.