This chapter provides a personal view on some recent concepts and methods of statistics of extremes, and discusses the challenges and opportunities could lead to potential future developments. Measure-dependent measures are here introduced as a natural probabilistic concept for modeling bivariate extreme values, and predictor-dependent spectral measures are discussed as a natural concept for modeling extremal dependence structures, which vary according to a covariate. Families of tilted measures are introduced as a unifying device connecting some recently proposed approaches. En passant, we discussed a new estimator for the so-called scedasis function.