There are three themes in my talk. In the first one, I discuss recent work on the transport of epithermal positrons across overlayers on metallic substrates. The second theme deals with the question of positronium formation and breakup at metallic surfaces. Finally, I present a new model for positron trapping at surfaces with a striking temperature dependence. This model is presented in detail in an adjoining paper and its tentative experimental verification has recently been published elsewhere.