Innovative and new computing paradigms must be considered as we reach the limits of von Neumann computing caused by the growth in necessary data processing. This paper provides an introduction to three emerging computing models that have established themselves as likely post-CMOS and post-von Neumann solutions. The first of these ideas is quantum computing, for which we discuss the challenges and potential of quantum computer architectures. Next, a computational system using intrinsic oscillators is introduced and an example is provided which shows its superiority in comparison to a typical von Neumann computational system. Finally, digital memcomputing using self-organizing logic gates is explained and then discussed as a method for optimization problems and machine learning.