For almost nearly a century, memory functions have been attributed only to acquired immune cells. Lately, this paradigm has been challenged by an increasing number of studies revealing that innate immune cells are capable of exhibiting memory-like features resulting in increased responsiveness to subsequent challenges, a process known as trained immunity (known also as innate memory). In contrast, the refractory state of endotoxin tolerance has been defined as an immunosuppressive state of myeloid cells portrayed by a significant reduction in the inflammatory capacity. Both training as well tolerance as adaptive features are reported to be accompanied by epigenetic and metabolic alterations occurring in cells. While training conveys proper protection against secondary infections, the induction of endotoxin tolerance promotes repairing mechanisms in the cells. Consequently, the inappropriate induction of these adaptive cues may trigger maladaptive effects, promoting an increased susceptibility to secondary infections—tolerance, or contribute to the progression of the inflammatory disorder—trained immunity. This review aims at the discussion of these opposing manners of innate immune and non-immune cells, describing the molecular, metabolic and epigenetic mechanisms involved and interpreting the clinical implications in various inflammatory pathologies.