We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions
are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non--commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kaehler potential.