Cytokine storm syndromes represent a wide array of immune dysregulation disorders that are becoming increasingly common in oncology and critical care medicine owing to the rising incidence of chimeric antigen receptor T-cell (CAR-T) therapy and T-cell targeting bispecific antibodies. The most recognized of the treatment-induced hyperinflammatory complications is cytokine release syndrome (CRS), whereas hemophagocytic lymphohistiocytosis/macrophage activation syndrome (HLH/MAS) may be secondary to malignancy, infections, immunotherapies, or cellular therapies. Both diseases have distinct criteria for the diagnosis, yet they overlap clinically to such an extent in cases with progressive hyperinflammation, coagulopathy, cytopenias, marked increase in serum ferritin levels, hepatopathy, and multiorgan failure. Distinguishing severe CRS from secondary HLH/MAS, or even from a mixed form of these syndromes, is very challenging for an intensivist because the clinical picture of fever, shock, respiratory failure, cytopenias, elevated inflammatory biomarkers, and organ dysfunction might correspond to various other conditions, including sepsis, progression of the underlying disease, or treatment side effects. The recognition of immune effector cell-associated HLH-like syndrome (IEC-HS) further supports the continuum between CRS and HLH/MAS rather than separate entities. The present review highlights the immunopathogenesis and clinical aspects of CRS and HLH/MAS, discusses overlapping and distinctive features of both diseases, and describes diagnostic algorithms and critical care strategies. Particular attention is paid to clinical assessment, trends in ferritin and fibrinogen levels, organ dysfunction, exclusion of infections, and multidisciplinary decision making. Improved recognition of hyperinflammatory disorders is important for providing timely targeted therapy while avoiding excessive inflammation or unnecessary immunosuppression.