While the ultimate theory of quantum gravity is yet to be established, the study of effective theories and specific models that capture interesting quantum gravitational effects is very important. Current approaches to quantum gravity underscore the relevance of noncommutative and generalized geometry in this context. These powerful mathematical frameworks encode properties of the underlying fundamental theories and constrain the structure of effective theories, leading to generalized models of gravity. Specific models and their solutions are used to study quantum gravitational effects in black holes and cosmology and can shed light on questions regarding quantum information and causality.