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Indoor localization has recently and significantly attracted the interest of the research community mainly due to the fact that Global Navigation Satellite Systems (GNSSs) typically fail in indoor environments. In the last couple of decades, there have been several works reported in the literature that attempt to tackle the indoor localization problem. However, most of this work is focused solely on two-dimensional (2D) localization, while very few papers consider three dimensions (3D). There is also a noticeable lack of survey papers focusing on 3D indoor localization; hence, in this paper, we aim to carry out a survey and provide a detailed critical review of the current state of the art concerning 3D indoor localization including geometric approaches such as angle of arrival (AoA), time of arrival (ToA), time difference of arrival (TDoA), fingerprinting approaches based on Received Signal Strength (RSS), Channel State Information (CSI), Magnetic Field (MF) and Fine Time Measurement (FTM), as well as fusion-based and hybrid-positioning techniques. We provide a variety of technologies, with a focus on wireless technologies that may be utilized for 3D indoor localization such as WiFi, Bluetooth, UWB, mmWave, visible light and sound-based technologies. We critically analyze the advantages and disadvantages of each approach/technology in 3D localization.