Fracture under compression is one of the most commonly studied properties of geomaterials like concrete and rock, in particular since these materials reach their best performance in compression. The fracture process is however rather complex due to the heterogeneous structures of said materials. Over the years fundemental studies of fracture under compression have led to a much improved insight in the details of the fracture process depending on the actual composition of the material. Fracture can be described by means of a 4-stage fracture model, which included as most important aspects pre-peak cracking, which is stable and can be arrested by stiffer and stronger elements in the material structure, and post-peak cracking . The latter macroscopic cracks are basically un-stable and can only be arrested by measures at a structural scale, such as applying confining stress or by using positive geometries. The material structure cannot assist in the arrest of the large energetic cracks other than locally affecting the crack path. In the paper an overview is given of the fracture process in compression. Recently we embarked on studying compressive fracture using a simpler material structure, namely foamed hardened cement paste . Stiff aggregates that are normally included in normal concrete have been left-out; instead a larger than usual quantity of large pores is brought into the material, even up to 80%. Studying fracture processes in this simpler material system ultimately allows for a better understanding of the details of the pre-peak cracking process, which is considered more important than the post-peak process since it defines strength.