Historically, communication engineers have dealt with electromagnetic forms of communication for many decades. Molecular communication (MC) is a relatively new communication engineering paradigm where information is delivered by small message molecules. Among many different ways to realize a molecular communication system, diffusion-based MC in combination with advection, and sometimes with chemical reaction, has been the prevalent approach in the literature thus far. In order to efficiently design and analysis a diffusive MC system, simple yet sufficiently accurate channel models are needed. In this talk, we will first give a brief introduction to existing component-wise models of a MC system. Then we will introduce the major end-to-end channel models in diffusive MC literature, including the effects of release mechanisms, the physical channel, and reception mechanisms. After building up the channel model, we can use PDE or SDE methods to obtain analytic or approximated solutions of the channel model. These solutions are called channel impulse responses, which characterize the dynamics of linear time-invariant MC systems.