Let D be the open unit disk in the complex plane. Let u be an analytic function on the unit disk D and let $\varphi$ be an analytic self-map of D. The weighted composition operator $u C_&ob;\varphi&cb;$ is defined as follows: for an analytic function f on D, $(u C_&ob;\varphi&cb;)f(z)=u(z)f(\varphi(z))$. These operators can be considered as a combination of a multiplication operator (when $\varphi$ is the identity map) and a composition operator (when $u\equiv 1$). Weighted composition operators appear naturally. It is known that the isometries between the Hardy spaces $H^p$, $1\le p<\infty$, $p\neq 2$, are weighted composition operators. A similar result holds for the isometries on the Bergman space $L^p_a$. Both composition operators and multiplication operators have been extensively studied in recent decades. However, the study on weighted composition operators is still a new territory. Recently, M. Contreras and A. Hernadez-Diaz characterized bounded and compact weighted composition operators on Hardy spaces by using the Carleson measure. In this talk, we are going to characterize bounded, compact and Schatten class weighted composition operators on the Bergman space $L^2_a$ by using generalized Berezin transforms. An estimate of the essential norms of weighted composition operators on the Bergman space is also given. Most of our results remain true for the Hardy space and weighted Bergman spaces. This is a joint work with Zeljko Cuckovic.