During operation, all components of a gas-turbine unit (GTU), including the blading of the axial compressor, are affected by the flow in the GTU flowpath, which results in the development of defects and deterioration of the main performance characteristics (efficiency, effective power, etc.). One of the most serious defects is erosive wear since it can cause destruction of one blade or all the blades in the compressor. This can lead to preliminary removal of a GTU from operation. Therefore, the erosion resistance of compressor blades is one of the main parameters controlling the service life of a gas-turbine unit. That is why studies of the erosive wear of axial compressors during operation of GTUs are urgent. This paper provides a review of the available publications on the erosive wear of blades and vanes in an axial compressor of gas-turbine units. The major erosion mechanisms classified by the type of particulates acting on blade material are examined. The geometric parameters of the compressor blading are found whose change due to erosive wear can disturb the flow aerodynamics and deteriorate the performance of individual elements and the overall GTU. The main three lines of erosive wear studies may be listed as follows: prediction of erosive wear, assessment and prediction of erosion consequences, and development of protective measures to control erosion during operation of a gas-turbine unit. The most frequently examined and promising subjects of erosion studies are outlined as applicable to gas turbine and compressor machine building. The state-of-the-art of studies in this field is analyzed.