Construction of valid confidence sets (or equivalently p-values) is of paramount importance to any sound statistical study. Traditional methods such as Wald, bootstrap, or subsampling fail to yield reliable uniformly valid inference when the functionals or the statistical models are irregular. Although tailored resampling methods have been proposed for specific irregular problems, we believe no unified inference framework exists. In this talk, I will discuss three new frameworks for adaptive, robustly valid inference that collectively cover many of the common statistical problems. This talk is based on joint work with Sivaraman Balakrishnan, Larry Wasserman, Kenta Takatsu, and Woonyoung Chang.