In this paper the Mojette transforms class is described. After recalling the birth of the Mojette transform, the Dirac Mojette transform is recalled with its basic properties. Generalizations to spline transform and to nD Mojette transform are also recalled. Applications of the Mojette transform demonstrate the power of frame description instead of basis in order to match different goals ranging from image coding, watermarking, discrete tomography, transmission and distributed storage. Finally, new insights for the future trends of the Mojette transform are sketched.