Many gauge theories, such as 3+1d and 2+1d SU(N) gauge theories with N_f massless Dirac fermions in the fundamental representation, exhibit "conformal windows" - a range of values of N_f for which the theory flows to a non-trivial conformal field theory at low energy. It is interesting to ask how these windows end and transition into phases with confinement and with spontaneous breaking of the flavor symmetry. I will begin by reviewing what is known about 3+1 dimensional QCD, focusing on the large N and N_f limit and on the conformal window there, and I will review the standard "merger scenario" for the end of its conformal window. I will then move on to QCD in 2+1 dimensions, and discuss its phase diagram as a function of the mass and of the discrete parameters N, N_f and the Chern-Simons level k, focusing again on the limit of large N, N_f, k. I will argue that this theory also has a conformal window (corresponding to a second order phase transition when changing the mass) but that it does not always end at a merger, and I will suggest two other possibilities for the end of general conformal windows. The different scenarios can be distinguished by the behavior of the theory as the boundary of the conformal window is approached from either side. Based on work in progress with Thomas Dumitrescu, Zohar Komargodski and Jiangyuan Qian.