Abstract: Most of the achievability proofs in Information theory are based on the concept of typicality. However, this typicality technique does not seem to be good enough to give achievability bounds in the most general settings, i.e. in the one-shot or non-iid case. In this talk we will discuss a hypothesis testing technique for proving inner bounds for some information theoretic problems. In particular, we will discuss about using hypothesis testing technique to prove achievable rates for point to point and multiple access channel. If time permits we will also discuss the extension of this technique in the quantum case, i.e., when the classical message is sent over the quantum channel.