Exactly three decades ago, it was realized that an accretion flow onto a black hole should be transonic. Since then, the subject has matured considerably and several new and well established concepts and methodologies have replaced earlier ways of studying accretion and winds. Not surprisingly, with the advent of the faster computers as well as better space-based telescopes, the results of numerical simulations and the observations have also improved along with the theory. Today, it is more than satisfying that the results of theory and numerical simulations, even in the context of nonmagnetic flows, agree in details of the observations exceedingly well. I present here several new concepts and intricacies which one has to get familiar with when one talks about the behavior of the transonic flows, either in accretion or in the outflows.