In this paper we review the mapping of continuum percolation on an off-lattice Potts model. This mapping shows that the continuum percalation transition, despite the differences with lattice percolation, is indeed a second order phase transition. Having posed these secure theoretical grounds we show that in major continuum systems, the percolation threshold can be derived analytically. These results are shown to be useful for systems containing non-trivial objects shapes and non-trivial interactions. Throughout the review we emphasize the equivalence of the concepts of the total excluded volume and the concept of the average critical number of bonds per object. We then mention the many real systems and fields of science for which the present results are relevant.