There has been much recent interest in understanding the dynamics of low-Reynolds-number swimmers near no-slip boundaries and free capillary surfaces. This talk will present theoretical ideas for studying the dynamics of such swimmers within the framework of simple two dimensional models. The 2D models are developed using the methods of complex analysis and afford significant analytical advantages while still capturing the essential mechanisms of (certain) fully three dimensional situations. In many cases the approach yields explicit nonlinear dynamical systems that can be directly studied. The models can rationalize behaviour observed in numerical and laboratory experiments and can provide predictions for the swimmer dynamics in more complicated situations. We will survey results on swimming near a no-slip wall [joint work with Y. Or], swimming in other conned geometries [joint work with O. Samson] and swimming near a free capillary surface [joint work with S. Lee, O. Samson, A. Hosoi and E. Lauga].