Approximate Bayesian deep learning methods hold significant promise for addressing several issues that occur when deploying deep learning components in intelligent systems, including mitigating the occurrence of over-confident errors and providing enhanced robustness to out of distribution examples. However, the computational requirements of existing approximate Bayesian inference methods can make them ill-suited for deployment in intelligent IoT systems that include lower-powered edge devices. In this paper, we present a range of approximate Bayesian inference methods for supervised deep learning and highlight the challenges and opportunities when applying these methods on current edge hardware. We highlight several potential solutions to decreasing model storage requirements and improving computational scalability, including model pruning and distillation methods.