New 2HDM symmetries were recently discovered, by proving that certain relations among the parameters of the scalar potential are preserved to all orders under renormalization for scalar and gauge interactions, and at least up to two-loops when considering Yukawa interactions. Models where such symmetries are imposed have interesting phenomenological aspects, which will be presented in this talk. In particular, I will show that explicit CP violation is possible for the simplest symmetry; that spontaneous breaking of symmetries such as CP, $Z_2$ or U(1) becomes impossible at tree-level; that all models containing these symmetries cannot have a decoupling limit; and that tree-level mass degeneracies found in the model will be lifted by loop corrections, providing a natural explanation for eventual small mass splittings between CP-even and CP-odd scalars.