The apparent simplicity of amorphous sphere packings can be misleading. Although random close packing is a common phenomenon that has been studied for decades recent theoretical and computational advances reveal how complex the underlying physics actually is. By bringing together perspectives from thermodynamics constraint satisfaction problems and optimization unique insights emerge. This chapter reviews these advances and describes a framework for addressing some of the remaining open problems including how to define a more rigorous analogue to random close packing and how to compute its properties.
