Despite the current boost in the use of electric vehicles to reduce the automotive sector’s footprint, combustion vehicles are and will be present in our cities in both the immediate and long term. In this sense, catalytic converters, which are exhaust gas post-treatment systems for vehicle emission control, are critical for complying with increasingly stringent environmental regulations. This work proposes a systematic review to identify the most relevant knowledge regarding the parameters (materials, geometries, and engine conditions), conditions (cold start, oxygen storage, and deactivation), and mathematical models to consider in the design of catalytic converters. The Scopus database contains 283 records related to this review’s objective. After applying the inclusion and exclusion criteria, 65 reports were retrieved for evaluation. A table was created to present the results and prepare this manuscript. The evaluation revealed that the following topics were active: the study of non-noble catalyst materials, as well as new substrate materials and geometries, for designing more compact and cost-effective catalytic converters; the development of strategies to improve conversion during cold starts; and the development of accurate and fast estimation models.