This primer describes the general model independent searches for new physics phenomena beyond the Standard Model of particle physics. First, the motivation for performing general model independent experimental searches for new physics is presented by giving an overview of the current theoretical understanding of particle physics in terms of the Standard Model of particle physics and its shortcomings. Then, the concept and features of general model independent search for new physics at collider based experiments is explained. This is followed by an overview of such searches performed in past high energy physics experiments and the current status of such searches, particularly in the context of the experiments at the LHC. Finally, the future prospects of such general model independent searches, with possible improvements using new tools such as machine learning techniques, is discussed.