After obtaining a finite element solution, we often want to estimate the error in the solution known as a-posteriori error estimation. Several techniques have been developed to provide estimates and bounds for the solution error in a specified norm or a quantity of interest. The effectiveness of some a-posteriori error estimators has resulted in efficient algorithms of the adaptive finite element method where either the mesh is locally refined (h-method) or a higher order polynomial is used (p-method). Such type of adaptive method is necessary for the real-life numerical simulation where the mesh size becomes too large for computation. Various types of a-posteriori error estimation techniques are presented in this chapter.