Quaternion Hyperbolic Transforms of the Fourier type, associated with quaternion-valued signals defined over an open rectangle of the Euclidean plane equipped with a hyperbolic measure, encompass the Fourier, Wigner-Ville, and linear canonical transforms. In this paper, we give a comprehensive review of these generalized transforms and provide some of their important properties. The different forms of the hyperbolic kernels of such transforms contain hyperbolic spatial variables and frequency variables, along with two quaternion algebra generators that take over the role of imaginary units—an essential feature to maintain the separation between the two dimensions.