A review of the literature pertaining to building occupancy detection, counting, and tracking - three areas under the umbrella of building occupancy estimation - is presented with a focus on mathematical approaches and corresponding metrics. The idea is to provide the reader with a background on the hardware and techniques used for occupancy inference, subsequent to data collection, with emphasis placed on the algorithmic characterization of occupancy estimation. The various approaches employed by researchers to tackle the problem are surveyed and summarized, including: data collection, cleaning processes, algorithm utilization and categorization, as well as data structuring and organization. The scope of prediction and performance metrics are used to establish a benchmarking system through a comprehensive summary of (indoor) occupancy estimation, presented in the context of the mathematical tools utilized. (C) 2019 Published by Elsevier B.V.