The intriguing electronic, structural and spectroscopic effects observed in high-pressure experiments cannot be fully understood and appreciated, if experiments are carried out on a standalone basis. To complement high-pressure experiments, a cornucopia of computational tools have been developed. Some of these approaches have been the focus of previous review articles, e.g., simulation methods for molecules, crystals and biological systems under pressure. This review article presents and overview of ab initio computational methodologies spanning the entire range between the atomic scale and infinitely large periodic systems under pressure. The theoretical foundations of each of these computational tools are summarized (Section 2) and selected applications, demonstrating the capabilitiesand limitations of modern computational high-pressure chemistry, are pointed out (Section 3).