This review article provides an overview of some challenges that arise when developing new medical robotic microgrippers. The main challenges are due to miniaturization and are present in the manufacturing and assembly processes, the types of mechanisms, the biomaterials used, the actuation principles, and the compliance with some standards and regulations. The main medical fields where these microgrippers are used are in minimally invasive surgery (MIS) and biomedical applications. Therefore, taking these two large groups into account, this review presents a microgrippers classification according to the type of mechanism used (traditional rigid-body mechanisms and complaint mechanisms). Moreover, parameters such as applications, functionalities, degrees-of-freedom (DOF), sizes, range of motion, biomaterial used, and proposed methods are highlighted. The analysis of 27 microgrippers among commercial and developed by research institutes is presented.