The introduction of Assur Groups in kinematics dates back to the early 20th century, with the work of a Russian engineer and mathematician, Leonid Vladimirovich Assur. In 1910, Assur developed a systematic way to classify mechanisms based on their kinematic chains. He identified specific groups of linkages, now known as Assur Groups, that can be used to compose a generic planar mechanism. Assur’s work aimed to simplify the analysis of mechanisms, allowing engineers and designers to understand better and predict their behaviours. He defined these groups based on the types and sequences of used joints, which paved the way for a more structured approach to kinematic synthesis. Over the decades, Assur Groups have become a fundamental part of kinematic analysis and design, influencing various fields such as robotics, automation engineering, and mechanical design. They provide a framework for understanding complex motion systems and optimizing designs for specific tasks. Today, Assur Groups continue to be a key tool in the study and application of kinematics, facilitating the development of innovative mechanical systems. The paper outlines the history of the Assur Groups, focussing on the period from their origin to their applications in computational kinematics, arriving at their recent extensions.