This paper presents a thorough review of transmitarray devices particularly aiming antenna beamsteering, gathering some of the most relevant solutions published by the scientific community in the field. First, the background for realizing 1-D and 2-D antenna beamsteering with a transmitarray is introduced. Subsequently, several examples of unit-cells for transmitarray implementation and complete transmitarray designs presented in the literature are outlined. Each solution is analyzed in detail, identifying the nature of its layout, e.g., based on microstrip patches, frequency selective surfaces (FSS), or metamaterials (MMs), and the method employed to enable electronic reconfigurability, e.g., p-in diodes, varactor diodes, or microelectromechanical systems (MEMS). In addition, some models with the capability of controlling the wavefront polarization modes are also included herein since these are the base of hybrid transmitarrays, i.e., transmitarray with both electronic beamsteering and polarization control. Finally, all the models are compared against each other in order to highlight their benefits and limitations, summarizing their main characteristics, such as the frequency of operation and bandwidth, insertion loss, physical dimensions, and maximum beamsteering range, when available.