Uncertainty quantification plays a central role in statistics and many other fields including physics, astronomy, epidemiology, and genomics. Indeed, any statistical procedure without quantifying its accuracy has only limited practical applicability, since one does not know how well the method works. >> In this talk, we consider construction of confidence sets in a range of settings, from the binomial proportion in classical statistics, to nonparametric regression with or without shape constraint, to high-dimensional linear regression. The results show significant differences between uncertainty quantification and optimal point estimation — the former is typically much harder than the latter, especially with respect to adaptivity to smoothness or sparsity