High performance computing (HPC) is taking an increasingly important place in drug discovery. It makes possible the simulation of complex biochemical systems with high precision in a short time, thanks to the use of sophisticated algorithms. It promotes the advancement of knowledge in fields that are inaccessible or difficult to access through experimentation and it contributes to accelerating the discovery of drugs for unmet medical needs while reducing costs. Herein, we report how computational performance has evolved over the past years, and then we detail three domains where HPC is essential. Molecular dynamics (MD) is commonly used to explore the flexibility of proteins, thus generating a better understanding of different possible approaches to modulate their activity. Modeling and simulation of biopolymer complexes enables the study of protein-protein interactions (PPI) in healthy and disease states, thus helping the identification of targets of pharmacological interest. Virtual screening (VS) also benefits from HPC to predict in a short time, among millions or billions of virtual chemical compounds, the best potential ligands that will be tested in relevant assays to start a rational drug design process.