This paper examines and contrasts two closely related evolutionary explanations in human behaviour: signalling theory, and the theory of Credibility Enhancing Displays. Both have been proposed to explain costly, dangerous, or otherwise ‘extravagant’ social behaviours, especially in the context of religious belief and practice, and each have spawned significant lines of empirical research. However, the relationship between these two theoretical frameworks is unclear, and research which engages both of them is largely absent. In this paper we seek to address this (...) gap at the theoretical level, examining the core differences between the two approaches and prospects and conditions for future empirical testing. We clarify the dynamical and mechanistic bases of signalling and CREDs as explanatory models and contrast the previous uses to which they have been put in the human sciences. Because of idiosyncrasies regarding those uses, several commonly supposed differences and comparative advantages are actually misleading and not in fact generalisable. We also show that signalling and CREDs theories as explanatory models are not interchangeable, because of deep structural differences. As we illustrate, the proposed causal networks of each theory are distinct, with important differences in the endogeneity of various phenomena within each model and their explanatory targets. As a result, they can be seen as complementary rather than in competition. We conclude by surveying the current state of the literature and identifying the differential predictions which could underpin more comprehensive empirical comparison in future research. (shrink)