Many dark energy (DE) models are based on a scalar field with timelike gradient while black holes (BHs) serve as probes of strong gravity. In this talk we begin with a review of the systematic construction of the effective field theory (EFT) describing perturbations around the Minkowski background with a timelike scalar profile and its extension to cosmological backgrounds, i.e. the ghost condensation and the EFT of inflation/DE. We then extend the EFT to arbitrary backgrounds. In this framework a set of consistency relations among EFT coefficients ensures the spatial diffeo invariance. Finally, we discuss applications of the general EFT to study perturbations of BH with a timelike scalar field responsible for DE.