Innate and adaptive immune responses have a well-known link and represent the distinctive origins of several diseases, many of which may be the consequence of the loss of balance between these two responses. Indeed, autoinflammation and autoimmunity represent the two extremes of a continuous spectrum of pathologic conditions with numerous overlaps in different pathologies. A common characteristic of these dysregulations is represented by hyperinflammation, which is an exaggerated response of the immune system, especially involving white blood cells, macrophages, and inflammasome activation with the hyperproduction of cytokines in response to various triggering stimuli. Moreover, hyperinflammation is of great interest, as it is one of the main manifestations of COVID-19 infection, and the cytokine storm and its most important components are the targets of the pharmacological treatments used to combat COVID-19 damage. In this context, the purpose of our review is to provide a focus on the pathogenesis of autoinflammation and, in particular, of hyperinflammation in order to generate insights for the identification of new therapeutic targets and strategies.