The ob­ject­ive of a ren­der­ing al­gorithm is to com­pute a pho­to­graph of a sim­u­lated real­ity, which en­tails find­ing all the paths along which light can flow from a set of light sources to the cam­era. The pur­pose of this art­icle is to present a high-level over­view of the un­der­ly­ing phys­ics and ana­lyze how this leads to a high-di­men­sion­al in­teg­ra­tion prob­lem that is typ­ic­ally handled us­ing Monte Carlo meth­ods. Fol­low­ing this, we sur­vey re­cent work on path space Markov Chain Monte Carlo (MCMC) meth­ods that com­pute the res­ult­ing in­teg­rals us­ing pro­pos­al dis­tri­bu­tions defined on sets of light paths.