Recently introduced concept of active non-Foster metamaterial is reviewed with an emphasis on the counterintuitive background physics. The main fundamental and technological limitations such as stability and selection criteria for active elements are highlighted. It is shown that non-Foster-based active metamaterials are stable if equivalent permittivity or permeability is positive number. Since this number can be (almost) arbitrarily small, the construction of practical broadband ENZ or MNZ metamaterials is feasible. Several examples of extremely broadband (bandwidth of more than two octaves) 1D and 2D active ENZ metamaterials developed at University of Zagreb are presented.