Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete-time Fourier transform and the Z-transform, from discrete time to continuous frequency, and the Fourier series, from continuous time to discrete frequency, are outside the class of discrete transforms.
Classical signal processing deals with one-dimensional discrete transforms. Other application areas, such as image processing, computer vision, high definition television, visual telephony, etc. make use of two-dimensional and in general, multidimensional discrete transforms.