The elliptic genera of 2d (0,4) SCFTs for the BPS strings in 6d (1,0) SCFTs have been extensively studied in the past decade. By geometric engineering, they are equivalent to the refined topological string partition function on the underlying elliptic non-compact Calabi-Yau threefolds. Some 6d SCFTs allow twisted circle compactification, for example when the gauge algebra has an outer automorphism. In such cases, the elliptic genera can be generalized to twisted elliptic genera which have many extraordinary properties. We systematically study the twisted elliptic genera including their localization, Higgsing, modular bootstrap, spectral flow symmetry and twisted elliptic blowup equations. This is based on a joint work with Kimyeong Lee and Xin Wang.