The objective of this paper is to review experimental and analytical investigations concerning the effect of the presence of solid particles on the performance of turbomachines. Experimental data on the effect of solid particles on turbine and compressor performance are examined. Some basic data have been reinterpreted to provide guidance for future design. The equations that govern the dynamics of the three-dimensional motion of solid particles suspended in compressible gas flow through a rotating cascade of a turbine are discussed. The results obtained from the solution of these equations are presented to indicate the location on the turbine blade subjected to erosion damage. Some erosion data relevant to gas turbine engines are discussed. The concluding remarks include a global view of the state of the art of particulate flow problems in turbomachinery.