I have always been fascinated by distribution-free non-parametric tests, or randomization tests, or Monte Carlo tests -- whatever you want to call them. (For example, I used some in ancient work like Diebold-Rudebusch 1992.) They seem almost too good to be true: exact finite-sample tests without distributional assumptions! They also still seem curiously underutilized in econometrics, notwithstanding, for example, the path-breaking and well-known contributions over many decades by Jean-Marie Dufour, Marc Hallin, and others.
For the latest, see the fascinating new contribution by Jean-Marie Dufour and Richard Luger. They show how to use randomization to perform simple tests of the null of linearity against the alternative of Markov switching in dynamic environments. That's a very hard problem (nuisance parameters not identified under the null, singular information matrix under the null), and several top researchers have wrestled with it (e.g., Garcia, Hansen, Carasco-Hu-Ploberger). Randomization delivers tests that are exact, distribution-free, and simple. And power looks pretty good too.