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This paper reviews control architectures for building heating, ventilation and air-conditioning (HVAC) systems, addressing the tension among energy demand, occupant comfort and equipment operability, and situating proportional-integral-derivative (PID) regulation within a layered control stack that also includes rule-based and model-based supervisory control and data-driven reinforcement learning (RL). It examines the thermostat-PID layer from two-position and scheduled setpoint control through proportional, PI and PID regulation and their tuning, then formulates RL for building control as a Markov decision process. Its central contribution is a taxonomy of where RL meets PID: RL as a gain tuner for an existing loop, as a direct replacement for the regulatory controller, as a hybrid with model predictive control, and as supervisory setpoint and schedule generation. Across these classes, the review establishes that the physical loop remains invariant while the intervention point changes, and that the classes differ in their requirements for actuation authority, state information, modelling, commissioning and constraint handling. It further establishes that PID is inexpensive and…