Aspects of the structural mechanics, vibration dynamics and rotor dynamics of compressors including impeller manufacture are described. The background knowledge required to understand the key structural issues is given with some simple analytic solutions. These identify the effects of blade thickness and blade taper on the stresses and the vibration characteristics of impellers. Such analytical solutions are only available for the simplest geometrical cases but give an insight into the fundamentals. Complex computer-based methods are used for the more detailed mechanical analysis of blades. A brief introduction to rotordynamics is also presented with the intention to guide the engineering of robust vibration-free compressor shafts. The characteristics of a simple rotor assembly, known as the Jeffcott single mass rotor, are examined using the equations of motion. Some limits on multistage compressor design introduced by rotordynamics can be derived even on the basis of the simple Jeffcott rotor; for example, the shaft should be thick and short to achieve a high critical speed. More complex rotor assemblies again need to be analysed with computer-based methods which are readily available.