Direction of Arrival (DOA) estimation is one of the important subjects in communication and radar systems and diverse methods have been suggested to address this problem. These methods are divided into three main parts: classical and subspace and sparse signal processing based methods. In The most of the sparse based methods, it is needed to build a candidate dictionary of angles with high resolution to have an accurate DOA estimation. However, In the real world, the sources are not necessarily located on the atoms of the dictionary which results in DOA estimation error. Recently, dictionary learning is employed to address this issue. The idea is using dictionary learning to adapt the angles of atoms according to the observed signals . In this research, dictionary learning is studied and we extend the application of this idea to multiple snapshot cases. Another source of error in DOA estimation is the non-calibrated arrays. Employing dictionary learning approach, we also suggest a new method to combat degrading effects of non-idealities of the array such as gain-phase, coupling and displacement errors. In all of these applications the proposed method for updating the dictionary is based on parametric dictionary learning and we use simple gradient descent algorithm. Array failure is another topic which has been studied in this research and a new algorithm is suggested to solve this problem. We also generalize some of the results to the case of wideband DOA estimation. To show the superiority of the proposed algorithms, in each part of the thesis, various simulations are done in different scenarios with one or multiple snapshots. Keywords: Dictionary Learning, DOA Estimation, Calibration, Array Failure