I will show how three apparently different modified gravity theories (mimetic gravity, limiting curvature, and the cuscuton) are in fact equivalent. Mimetic gravity was first proposed as a singular disformal transformation of General Relativity, from which a dust-like perfect fluid that could mimic cold dark matter at the cosmological level appeared. Limiting curvature was hypothesised as an effective approach for resolving all space-time singularities. The cuscuton was defined by taking the incompressible limit of a scalar field/perfect fluid. All three theories will be shown to be essentially the same, and I will discuss possible physical implications.