Novel perovskites pertain to newly discovered or less studied variants of the conventional perovskite structure, characterized by distinctive properties and potential for diverse applications such as ferroelectric, optoelectronic, and thermoelectric uses. In recent years, advancements in computational methods have markedly expedited the discovery and design of innovative perovskite materials, leading to numerous pertinent reports. However, there are few reviews that thoroughly elaborate the role of computational methods in studying novel perovskites, particularly for state-of-the-art perovskite categories. This review delves into the computational discovery of novel perovskite materials, with a particular focus on antiperovskites and chalcogenide perovskites. We begin with a discussion on the computational methods applied to evaluate the stability and electronic structure of materials. Next, we highlight how these methods expedite the discovery process, demonstrating how rational simulations contribute to researching novel perovskites with improved performance. Finally, we thoroughly discuss the remaining challenges and future outlooks in this research domain to encourage further investigation. We believe that this review will be highly beneficial both for newcomers to the field and for experienced researchers in computational science who are shifting their focus to novel perovskites.