- In this paper we study the reception zones of a wireless network in the SINR model with receivers that employ interference cancellation (IC), a technique that allows a receiver to decode interfering signals, and cancel them from the received signal in order to decode its intended message. We first derive some important topological properties of the diagram describing the reception zones and their connections to high-order Voronoi diagrams and other related geometric objects. We then discuss the computational issues that arise when seeking an efficient description of the zones. Our main fundamental result states that although potentially there are exponentially many possible cancellation orderings (and consequently reception cells), in fact there are much fewer nonempty such cells. We prove a (tight) linear bound on the number of cells and provide a polynomial time algorithm to describe the diagram. Moreover, we introduce a novel measure, referred to as the Compactness Parameter, which influences the tightness of our bounds. We then utilize the properties established for reception diagrams to devise a logarithmic time algorithm for answering point-location queries for networks with IC.