A complex space X is said to be hyperbolic if every holomorphic map from the complex line to X is constant. It is conjectured that a generic complete intersection surface of general type is hyperbolic, and it is known that it holds for high degrees. But even examples for low degrees are hard to find. In a recent work with Natalia García, we proved existence of examples in every P^n with n ≥ 10, and we found infinite families in projective spaces of smaller dimensions. The technique was initiated by Vojta, which is based in ideas of Bogomolov, and it can be used with surfaces related to the surface of the cuboids. I will introduce the topic with those surfaces, trying to get into the key ideas for the construction of hyperbolic complete intersection surfaces.