Home computers are often considered as ‘domestic technology’ or part of the ‘domestic media ensemble’ as if those were simple and straightforward concepts. In this paper, we investigate the notions of domesticity and domestication and explore the processes of integration of the home computer into the domestic sphere. This paper starts with an exploration of the concept of domesticity. It then analyses how a family builds an image of the computer as a domestic or undomestic object. This analysis is based on a series of interviews with seven British families in the late 1990’s. This analysis is used to identify some of the characteristics that contribute to make the home computer domestic or undomestic, and to explore the processes of domestication.