Weighted automata and transducers are used in a variety of applications ranging from automatic speech recognition and synthesis to computational biology. They give a unifying framework for the representation of the components of complex systems. This provides opportunities for the application of general optimization algorithms such as determinization, epsilon-removal and minimization of weighted transducers. We give a brief survey of recent advances in language processing with weighted automata and transducers, including an overview of speech recognition with weighted transducers and recent algorithmic results in that field. We also present new results related to the approximation of weighted context-free grammars and language recognition with weighted automata.