The JAK/STAT signaling pathway plays a key role in cytokine signaling and is involved in development, immunity, and tumorigenesis for nearly any cell. At first glance, the JAK/STAT signaling pathway appears to be straightforward. However, on closer examination, the factors influencing the JAK/STAT signaling activity, such as cytokine diversity, receptor profile, overlapping JAK and STAT specificity among non-redundant functions of the JAK/STAT complexes, positive regulators (e.g., cooperating transcription factors), and negative regulators (e.g., SOCS, PIAS, PTP), demonstrate the complexity of the pathway’s architecture, which can be quickly disturbed by mutations. The JAK/STAT signaling pathway has been, and still is, subject of basic research and offers an enormous potential for the development of new methods of personalized medicine and thus the translation of basic molecular research into clinical practice beyond the use of JAK inhibitors. Gain-of-function and loss-of-function mutations in the three immunologically particularly relevant signal transducers STAT1, STAT3, and STAT6 as well as JAK1 and JAK3 present themselves through individual phenotypic clinical pictures. The established, traditional paradigm of loss-of-function mutations leading to immunodeficiency and gain-of-function mutation leading to autoimmunity breaks down and a more differentiated picture of disease patterns evolve. This review is intended to provide an overview of these specific syndromes from a clinical perspective and to summarize current findings on pathomechanism, symptoms, immunological features, and therapeutic options of STAT1, STAT3, STAT6, JAK1, and JAK3 loss-of-function and gain-of-function diseases.