This paper reviews the renormalization of soft supersymmetry breaking terms using the method of analytic continuation of couplings into superspace. Super-Feynman rules in the softly broken theory are derived. The renormalization group equation for the soft terms in the Wess-Zumino model and the supersymmetric gauge theories are explored and the dimensional reduction scheme is clarified. As applications, the leading results of the gauge-mediated supersymmetry breaking scenario are obtained and the effective potential along the flat direction in the theory containing the flat direction is discussed in this paper.
