Here, a gist of the basic, initial results associated with convexifactors in the literature are presented. We begin by defining convexifactors and establishing their relations with the other subdifferentials. Further, we talk about regularity, minimality and calculus rules for convexifactors. We also present mean value theorem and chain rule via convexifactors which play an important role in developing optimality conditions. After that, we characterize quasiconvex functions via quasimonotonicity of convexifactors. Further, we summarize results which characterize pseudoconvex and quasiconvex functions in terms of pseudomonotonicity and quasimonotonicity of convexifactors. Finally, we summarize the work done by various researchers in the literature for many interesting and complicated optimization problems.