There is tremendous hype around the burgeoning Internet of Things, and particularly in the industrial realm (the industrial Internet of Things, IIoT), where many expect to find the biggest opportunity in the near term. Beyond the hype, the conversation lacks a clear definition of what the IIoT is and the role of different players throughout the value chain. In this report, we will lay out a taxonomy for the IIoT that addresses three fundemental questions: What are we connecting? How are we connecting? and Why are we connecting? We will also outline common framework for understanding IIoT system topology. To better understand the function and value of IIoT systems, we will apply the taxonomy and framework to five case studies of deployed systems in different industries with different goals.