There are several reasons why galaxies and galaxy modellers care about Asymptotic Giant Branch stars. AGB stars trace the halo stellar distribution (see Demers in this volume), thus indicating what is the size and the dynamics of the system; they trace intermediate-age stars (see Grebel, this volume), thus showing if and how much star formation (SF) activity has occurred in the region 0.5 - 1 Gyr ago; they are the major site of production of several chemical elements (see Busso and Lattanzio in this volume) and fundamental contributors to the stellar nucleosynthesis yields, which, in turn, are the main ingredients of chemical evolution models.
This review is focussed on the third point, which is the most important one for chemo-dynamical models of galaxy evolution. Let me however mention how important it is to trace intermediate age and old populations. IZw18 is the most metal poor star-forming galaxy ever discovered. Being very blue and full of gas, it was often considered a local counterpart of primeval galaxies and a really young system, with SF activity begun only a few Myr ago. However, when HST optical photometry became available, AGB stars were found [Aloisi, Tosi, & Greggio (1999)] and then confirmed with near-infrared HST photometry [Ostlin (2000)]. The presence of AGB stars undisputably demonstrated that IZw18 is not as young as originally thought and must have started forming stars at least 0.5 - 1 Gyr ago.
Here, I will describe the effects of AGB stars as interstellar medium (ISM) polluters with reference to the evolution of a few interesting elements: 3He, 4He, 12C, 13C, N and Na. The galaxy evolution models described here are all standard, in the sense that they do not explicitely treat dynamical aspects. It is however becoming increasingly clear that to understand galaxy evolution dynamical and hydrodynamical effects cannot be left aside.