Despite the numerous benefits for preserving the hydrological cycle, permeable pavement systems (PPSs) found their major application in parking spots and for light traffic scenarios due to their limited durability and strength. To make the PPSs suitable for heavy traffic conditions without significant distresses, research is shifting toward the adoption of novel binders and additives for designing multifunctional porous asphalt mixtures which make up the surface course of PPSs. Certain additives are well known for enhancing the durability of dense graded asphalt mixtures and improving fatigue and rutting resistance. However, the studies on the influence of additives on abrasion resistance and binder draindown, which are the common problems in porous asphalt mixtures (PAMs), are still not well established. This paper summarizes best practices performed on PAMs and recommends possible future research directions for its improvement. Particular emphasis is placed on strength and resilience of PAMs by incorporating additives like nanosilica, crumb rubber, warm-mix additives, fibers (such as cellulose, glass, steel, and synthetic fibers), and some eco-friendly materials. It was found that different additives seem to have different effects on the properties of PAMs. Moreover, the combination of additives has synergistic benefits for the performance of PAMs, especially in urban pavements.