Wireless communications are significantly impacted by the propagation environment, particularly in doubly selective channels with variations in both time and frequency domains. Orthogonal Time Frequency Space (OTFS) modulation has emerged as a promising solution; however, its high equalization complexity, if performed in the delay-Doppler domain, limits its universal application. This article explores domain-adaptive system design, with an emphasis on adaptive equalization, while also discussing modulation and pilot placement strategies. It investigates the dynamic selection of best-fit domains based on channel conditions to enhance performance across diverse environments. We examine channel domain connections, signal designs, and equalization techniques with domain adaptivity, and highlight future research opportunities.