Probabilistic reasoning is now routinely used in many fields of science and engineering, where it underlies systems that perform tasks such as text classification, social network analysis, medical diagnosis, information extraction, probabilistic planning, vision and robotics. This project aims to develop an anytime and generalized probabilistic inference engine that targets a wide range of probabilistic representations, including classical, propositional representations --- such as Bayesian and Markov networks --- in addition to more expressive representations based on first order logic. The project will also investigate probabilistic queries in complexity classes that have not received much attention in the literature, yet can be used to study the robustness of inferences and decisions based on probabilistic reasoning systems. The targeted inference engine is planned to put the state of the art in exact inference at the service of approximate inference, allowing it to resign to approximations only when exact inference yields. Moreover, the engine is planned to smoothly and incrementally improve its approximations over time. A key emphasis of the project is to accomplish these objectives while using the most general probabilistic representation as an input, to allow for the widest possible adoption of the developed inference engine. Our anticipated results will impact many fields by allowing users to perform more accurate probabilistic inference, on larger models and in different contexts. Through scientific articles, research seminars, conference presentations, and graduate teaching, we expect the obtained results to be widely disseminated so as to maximize the attained benefits by various communities. Moreover, we plan to publicly release software systems that embed our results, continuing with a long tradition of publicly releasing award-winning software systems for probabilistic reasoning.