Inborn errors of immunity (IEI) or primary immune deficiencies (PIDD) are caused by variants in genes encoding for molecules that are relevant to the innate or adaptive immune response. To date, defects in more than 450 different genes have been identified as causes of IEI, causing a constellation of heterogeneous clinical manifestations ranging from increased susceptibility to infection, to autoimmunity or autoinflammation. IEI that are mainly characterized by autoinflammation are broadly classified according to the inflammatory pathway that they predominantly perturb. Among autoinflammatory IEI are those characterized by the transcriptional upregulation of type I interferon genes and are referred to as interferonopathies. Within the spectrum of interferonopathies, genetic defects that affect the proteasome have been described to cause autoinflammatory disease and represent a growing area of investigation. This review is focused on describing the clinical, genetic, and molecular aspects of IEI associated with mutations that affect the proteasome and how the study of these diseases has contributed to delineate therapeutic interventions.