Algebraic effects with handlers provide a convenient mechanism for managing multiple computational effects. One particular approach to the implementation of algebraic effects is known as the capability-passing style, in which effectful operations can be performed by using a regular first-class value which is provided by a handler. During the talk we will propose a calculus of effect capabilities and discuss the challenges involved in designing logical relations for it. We will present two models, of which one scales well to various language features, and the other exposes a connection between handlers and delimited control. Finally, we will demonstrate the utility of our models by proving a few non-trivial program equivalences.