In this paper, we present a detailed study and comparison of different classification algorithms. Our main purpose is the study of the Vicinal Support Vector Classifier (VSVC) and its relations to the other state-of-the-art classifiers. To this end, we start by the historical development of each classifier, derivation of the mathematics behind it and describing the relations that exist between some of them, in particular the relation between the VSVC and the other classifiers. Thereafter, we apply them to two famous learning datasets very used by the research community, namely the MIT-CBCL face and the Wisconsin Diagnostic Breast Cancer (WDBC) datasets. We show that despite its simplicity compared to the other state-of-the-art classifiers, the VSVC leads to very robust classification results and provide some practical advantages compared to the other classifiers.