ClpXP is a AAA+ protease that uses the energy of ATP binding and hydrolysis to perform mechanical work during targeted protein degradation within cells. ClpXP consists of hexamers of a AAA+ ATPase (ClpX) and a tetradecameric peptidase (ClpP). Asymmetric ClpX hexamers bind unstructured peptide tags in protein substrates, unfold stable tertiary structure in the substrate, and then translocate the unfolded polypeptide chain into an internal proteolytic compartment in ClpP. Here, we review our present understanding of ClpXP structure and function, as revealed by two decades of biochemical and biophysical studies.