The problem of solving a system of possibly nonsmooth equations with nonisolated solutions appears in several applications. For example, complementarity problems, necessary conditions for generalized Nash equilibrium problems, or Karush-Kuhn-Tucker conditions of an inequality constrained optimization problem can be written in this way. An iterative framework for solving such systems and appropriate conditions for local superlinear convergence will be presented. Moreover, different algorithms belonging to the framework will be described. Particular emphasis is placed on the piecewise smooth case.