It is well-known that monoamine oxidase (MAO) plays a pivotal role in neurodegeneration and the inhibition of this enzyme can manifest antidepressant properties as well as have a positive impact in Alzheimer's and Parkinson's diseases. MAO has two isoforms: MAO-A and MAO-B. The main hMAO-B inhibitors used for the treatment of Alzheimer's and Parkinson's diseases, encompass a terminal triple bond in their structure, which provides their potency. Recently, a new class of inhibitors has emerged, bearing the carbon-carbon triple bond not necessarily at the end of the chain. In this review, the structure and physiological function of the MAO enzymes is discussed, the general synthetic procedures of propargylamines, as well as their mechanism of inhibition. Moreover, it is highlighted the current development and discovery of potential hMAO-B inhibitors from propargylamine scaffolds, showcasing their structure-activity relationships (SARs) with the enzyme. Conformational relationships' analysis is performed as well. Induced fit docking is performed, also, to the most potent compounds revealed in order to assess their binding energy and interactions with the enzyme. Finally, molecules which do not contain a propargylamine moiety in their structure were studied and compared against a known hMAO-B inhibitor, deprenyl. From the superimposition results of these molecules with deprenyl, as well as the interactions of the molecules with the amino acids of the active site of hMAO-B, it appears that these compounds have several similarities with deprenyl, opening new paths for the creation of novel molecules against Alzheimer's disease (AD).