A traditional cellular system (e.g., LTE) operates only on the licensed spectrum. This tutorial explains the concept of cellular communications on both licensed and license-exempt spectrum under a unified architecture. The purpose to extend a cellular system into the bandwidth-rich license-exempt spectrum is to form a larger cellular network for all spectrum types. This would result in an ultimate mobile converged cellular network. This tutorial examines the benefits of this concept, the technical challenges, and provides a conceptual LTE-based design example that helps to show how a traditional cellular system like the LTE can adapt itself to a different spectrum type, conform to the regulatory requirements, and harmoniously co-exist with the incumbent systems such as Wi-Fi. In order to cope with the interference and regulation rules on license-exempt spectrum, a special medium access mechanism is introduced into the existing LTE transmission frame structure to exploit the full benefits of coordinated and managed cellular architecture.