Minimally modified gravity models are a class of modified gravity theories with only two local degrees of freedom as in General Relativity. In this seminar I want to discuss their general properties such as the existence of a preferred foliation and then discuss phenomenological applications in the early Universe. While during inflation the modifications to the power spectra are slow-roll suppressed, for the bispectrum we can get new signatures deviating from standard single scalar field models. Further, I will discuss how these models can be used to construct stable and viable bouncing scenarios.