The Internet of Things (IoT) refers to a pervasive presence of interconnected and uniquely identifiable physical devices. These devices' goal is to gather data and drive actions in order to improve productivity, and ultimately reduce or eliminate reliance on human intervention for data acquisition, interpretation, and use. The proliferation of these connected low-power devices will result in a data explosion that will significantly increase data transmission costs with respect to energy consumption and latency. Edge computing reduces these costs by performing computations at the edge nodes, prior to data transmission, to interpret and/or utilize the data. While much research has focused on the IoT's connected nature and communication challenges, the challenges of IoT embedded computing with respect to device microprocessors has received much less attention. This paper explores IoT applications' execution characteristics from a microarchitectural perspective and the microarchitectural characteristics that will enable efficient and effective edge computing. To tractably represent a wide variety of next-generation IoT applications, we present a broad IoT application classification methodology based on application functions, to enable quicker workload characterizations for IoT microprocessors. We then survey and discuss potential microarchitectural optimizations and computing paradigms that will enable the design of right-provisioned microprocessors that are efficient, configurable, extensible, and scalable. This paper provides a foundation for the analysis and design of a diverse set of microprocessor architectures for next-generation IoT devices.