  We review the background field method for three-dimensional Yang-Mills and
Chern-Simons models in N=2 superspace. Superfield proper time (heat kernel)
techniques are developed and exact expressions of heat kernels for constant
backgrounds are presented. The background field method and heat kernel
techniques are applied for evaluating the low-energy effective actions in N=2
supersymmetric Yang-Mills and Chern-Simons models as well as in N=4 and N=8 SYM
theories.
