In this papers, we highlight recent work done on one of the most fundamental problems in computational chemistry, Crystal Structure Prediction. In CSP, the goal is to find a configuration of ions in 3D space that yields the lowest (i.e. the greatest negative) pairwise potential energy. This problem has only recently been formalised as a mathematical problem, leaving many interesting open problems. This abstract will highlight the recent work between computer science and chemistry, as well as presenting several interesting open problems. In particular, we show that this problem is undecidable in the general case and NP-hard when the size of the period defining the crystal is given. Further, we give an overview of the combinatorial results on these structures that may provide future tools for solving this problem in some restricted cases. Finally, we provide an integer programming model for solving this problem in the case of a fixed-size period.