Recently, much interest has been directed towards software defined radios and embedded intelligence in telecommunication devices. However, no theoretical framework for cognitive radios has ever been proposed. In this paper, we introduce an information theoretic point of view on cognitive radios. Specifically, our motivation in this work is to embed humanlike intelligence in mobile wireless devices, following the three century-old work on Bayesian probability theory, the maximum entropy principle and minimal probability update. This allows us to partially answer such questions as “what are the signal detection capabilities of a wireless device?” or “when facing a situation in which most parameters are missing, how to react?”. As an introduction, we will present two examples from the same authors using the cognitive framework namely multi-antenna channel modelling and signal sensing.