Towards a sustainable energy future, it is essential to develop new catalysts with improved properties for key catalytic systems such as Haber-Bosch process, water electrolysis and fuel cell. Unfortunately, the current state-of-the-art catalysts still suffer from high cost of noble metals, insufficient catalytic activity and long-term stability. Furthermore, the current strategy to develop new catalysts relies on “trial-and-error” method, which could be time-consuming and inefficient. To tackle this challenge, atomic-level simulations have demonstrated the potential to facilitate catalyst discovery. For the past decades, the simulations have become reasonably accurate so that they can provide useful insights toward the origin of experimentally observed improvements in catalytic properties. In addition, with the exponential increase in computing power, high-throughput catalyst screening has become feasible. More excitingly, recent advances in machine learning have opened the possibility to further accelerate catalyst discovery. Herein, we introduce recent applications and challenges of computation and machine learning for catalyst discovery.