Presentation attack detection (PAD) is used to mitigate the dangers of the weakest link problem in biometric recognition, in which failure modes of one application affect the security of all other applications. Strong PAD methods are therefore a must, and we believe biometric challenge-response protocols (BCRP) form an underestimated part of this ecosystem. In this paper, we conceptualize what BCRPs are, and we propose a descriptive formalism and categorization for working with them. We validate the categorization against existing literature that we classified to be describing BCRPs. Lastly, we discuss how strong BCRPs provide advantages over PAD methods, specifically in the protection of individual applications and the protection of other applications from inadvertent leaks in BCRP applications. We note that research in BCRPs is fragmented, and our intent for the proposed formalism and categorization are to give focus and direction to research efforts into biometric challenge-response protocols.