The problem of the sphere rolling on a plane is one of the most classical examples of nonholonomic mechanical systems. I will use this example to give a brief introduction to this kind of systems, their properties, and the main tools that are used to study them which go from geometry and dynamics to symmetries and Lie groups. We will then consider classical and new affine variations of this problem and see that the dynamics ranges from integrable to chaotic depending on the specifics of the system. Finally, I will discuss some curious and surprising phenomena occurring in specific examples.