Robotics systems are now increasingly widespread in our day-life. For instance, robots have been successfully used in several fields, like, agriculture, construction, defense, aerospace, and hospitality. However, there are still several issues to be addressed for allowing the large scale deployment of robots. Issues related to security, and manufacturing and operating costs are particularly relevant. Indeed, differently from industrial applications, service robots should be cheap and capable of operating in unknown, or partially-unknown environments, possibly with minimal human intervention. To deal with these challenges, in the last years the research community focused on deriving learning algorithms capable of providing flexibility and adaptability to the robots. In this context, the application of Machine Learning and Reinforcement Learning techniques turns out to be especially useful. In this manuscript, we propose different learning algorithms for robotics systems. In Chapter 2, we propose a solution for learning the geometrical model of a robot directly from data, combining proprioceptive measures with data collected with a 2D camera. Besides testing the accuracy of the kinematic models derived with real experiments, we validate the possibility of deriving a kinematic controller based on the model identified. Instead, in Chapter 3, we address the robot inverse dynamics problem. Our strategy relies on the fact that the robot inverse dynamics is a polynomial function in a particular input space. Besides characterizing the input space, we propose a data-driven solution based on Gaussian Process Regression (GPR). Given the type of each joint, we define a kernel named Geometrically Inspired Polynomial (GIP) kernel, which is given by the product of several polynomial kernels. To cope with the dimensionality of the resulting polynomial, we use a variation of the standard polynomial kernel, named Multiplicative Polynomial kernel, further discussed in Chapter 6. Tests performed on simulated and real environments ...