Cocktail party problem is a classical scientific problem that has been studied for decades. Humans have remarkable skills in segregating target speech from a complex auditory mixture obtained in a cocktail party environment. Computational modeling for such a mechanism is however extremely challenging. This chapter presents an overview of several recent techniques for the source separation issues associated with this problem, including independent component analysis/blind source separation, computational auditory scene analysis, model-based approaches, non-negative matrix factorization and sparse coding. As an example, a multistage approach for source separation is included. The application areas of cocktail party processing are explored. Potential future research directions are also discussed.