Even though current micro-nano fabrication technology has reached integration levels where ultra-sensitive sensors can be fabricated, the sensing performance (resolution per joule) of synthetic systems are still orders of magnitude inferior to those observed in neurobiology. For example, the filiform hairs in crickets operate at fundamental limits of noise; auditory sensors in a parasitoid fly can overcome fundamental limitations to precisely localize ultra-faint acoustic signatures. Even though many of these biological marvels have served as inspiration for different types of neuromorphic sensors, the main focus these designs have been to faithfully replicate the biological functionalities, without considering the constructive role of "noise". In man-made sensors device and sensor noise are typically considered as a nuisance, where as in neurobiology "noise" has been shown to be a computational aid that enables biology to sense and operate at fundamental limits of energy efficiency and performance. In this paper, we describe some of the important noise-exploitation and adaptation principles observed in neurobiology and how they can be systematically used for designing neuromorphic sensors. Our focus will be on two types of noise-exploitation principles, namely, (a) stochastic resonance; and (b) noise-shaping, which are unified within our previously reported framework called ΣΔ learning. As a case-study, we describe the application of ΣΔ learning for the design of a miniature acoustic source localizer whose performance matches that of its biological counterpart(Ormia Ochracea).