 This review provides a comprehensive overview of the literature on non-hermitian flukae topological matter in one and two spatial dimensions, including its exotic properties resulting from the interplay between driving fields and non-hermiticity. The authors introduce useful tools for studying these systems and present typical examples of non-hermitian flukae topological insulators, superconductors, and quasicrystals, highlighting their topological invariance, bulk edge correspondences, non-hermitian skin effects, dynamical properties, and localization transitions. The authors conclude by summarizing their main findings and presenting future directions for research. This article was authored by Longwen Zhou and Dijian Zhang.