The distributed coordination and control of a set of autonomous mobile robots is a problem widely studied in a variety of fields, such as engineering, artificial intelligence, artificial life, robotics. Generally, in this areas the problem is studied mostly from an empirical point of view. Recently, a significant research effort has been and continues to be spent on understanding the fundamental algorithmic limitations on what a set of autonomous mobile robots can achieve. By robot, we mean a physical device equipped with motorial capabilities, that allow it to move on a two dimensional plane, and with sensorial capabilities, that allow it to sense the presence of other robots in the plane. In particular, the focus is to identify the minimal robot capabilities (sensorial, motorial, computational) that allow a problem to be solvable and a task to be performed. In this talk we describe the current investigations on the interplay between robots capabilities, computability, and algorithmic solutions of the flocking and the intruder problem.