Functional claims about technical artefacts set a second stage on which theories of functions can prove themselves. We present a general framework for understanding theories of technical functions. In particular, we argue that theories of technical functions can be seen as sophisticated combinations of three archetypical accounts, which we call the intentional account, the causal-role account and the evolutionist account. These abstracted, general theories of functions apply to both biology and technology, all with their respective drawbacks and benefits. When focusing on technology these drawbacks and benefits appear complementary, suggesting that the archetypes can be combined into a tenable analysis of technical functions. We argue that straightforward combinations inherit the drawbacks of the archetypes or have new ones. Then, we show that three existing theories of technical functions – our own ICE theory and alternatives devised by Krohs and by Longy – can be taken as sophisticated combinations. In each theory, one of the archetypes is corrected by incorporating elements of the others. Finally, we consider the applicability of our three-archetype framework to function theories that apply to biology as well as to technology.@en