The algebraic classification of stress-energy tensors includes tensors whose symmetry is partly broken as compared with Einstein’s maximally symmetric cosmological term. This allows us to introduce, in a general setting, a vacuum dark fluid with variable density and pressures approaching the cosmological constant in certain space-time regions. The relevant class of Einstein equations describes cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy and compact objects with de Sitter interiors generically related to vacuum dark energy, which can be responsible for observational effects typical of dark matter. The mass of objects is generically related to breaking of space-time symmetry from the de Sitter group. We outline the basic generic properties of regular cosmological models with vacuum dark energy, and of dark matter candidates with de Sitter interiors, including their observational signatures.