Fungal infections, such as candidiasis caused by Candida, pose a problem of growing medical concern. In developed countries, the incidence of Candida infections is increasing due to the higher survival of susceptible populations, such as immunocompromised patients or the elderly. Existing treatment options are limited to few antifungal drug families with efficacies that vary depending on the infecting species. In this context, the emergence and spread of resistant Candida isolates are being increasingly reported. Understanding how resistance can evolve within naturally susceptible species is key to developing novel, more effective treatment strategies. However, in contrast to the situation of antibiotic resistance in bacteria, few studies have focused on the evolutionary mechanisms leading to drug resistance in fungal species. In this review, we will survey and discuss current knowledge on the genetic bases of resistance to antifungal drugs in Candida opportunistic pathogens. We will do so from an evolutionary genomics perspective, focusing on the possible evolutionary paths that may lead to the emergence and selection of the resistant phenotype. Finally, we will discuss the potential of future studies enabled by current developments in sequencing technologies, in vitro evolution approaches, and the analysis of serial clinical isolates.