Recent years have seen a substantial increase in the number of tools available to monitor and study HIV reservoirs. Here, we discuss recent technological advances that enable an understanding of reservoir dynamics beyond classical assays to measure the frequency of cells containing provirus able to propagate a spreading infection (replication-competent reservoir). Specifically, we focus on the characterization of cellular reservoirs containing proviruses able to transcribe viral mRNAs (so called transcription-competent) and translate viral proteins (translation-competent). We suggest that the study of these alternative reservoirs provides complementary information to classical approaches, crucially at a single-cell level. This enables an in-depth characterization of the cellular reservoir, both following reactivation from latency and, importantly, directly ex vivo at baseline. Furthermore, we propose that the study of cellular reservoirs that may not contain fully replication-competent virus, but are able to produce HIV mRNAs and proteins, is of biological importance. Lastly, we detail some of the key contributions that the study of these transcription and translation-competent reservoirs has made thus far to investigations into HIV persistence, and outline where these approaches may take the field next.