Parallel manipulators with lower mobility (LM-PMs) are multi-loop mechanisms with less than six degrees of freedom (dofs). This type of manipulators has attracted the attention both of academic researchers and of industries since the early appearance of the DELTA robot (Clavel 1988). The DELTA robot showed that, when the manipulation task requires less than six dofs, the use of an LM-PM may bring some advantages (simple architecture of the machine, very fast machine, etc.) that are added to the known appealing features (high stiffness, good positioning precision, etc) of parallel manipulators (PMs).Planar motions, translational motions and spherical motions are important examples of motion tasks that require less than six dofs and are often necessary in industrial applications. Each of these types of motion has generated a class of LM-PMs. So, today, there is a great variety of planar PMs (PPMs), of translational PMs (TPMs) and of spherical PMs (SPMs). This chapter attempts to provide a unified frame for the study of this type of machines together with a critical analysis of the vast literature about them. The chapter starts with the classification of the LM-PMs, and, then, analyzes the specific subjects involved in the functional design of these machines. Special attention is paid to the definition of the limb topology, the singularity analysis and the discussion of the characteristics of some machines.