Ultra-wideband (UWB) radio is a fast emerging technology with many unique attractive features that promotes major advances in wireless communications, networking, radar, imaging, and positioning systems. Research in UWB is still in its infancy stages, offering limited resources in handling the challenges facing the UWB communications. Understanding the unique properties and challenges of UWB communications as well as its application in competent signal processing techniques are vital in conquering the obstacles towards developing exciting UWB applications. UWB research and development has to cope with the challenges that limit their performance, capacity, throughput, network flexibility, implementation complexity, and cost. This tutorial focuses on UWB wireless communications at the physical layer. It overviews the state-of-the-art UWB in channel modeling, transmitters, and receivers of UWB radios, and outlines the research directions and challenges that needs to be overcome. Since a signal processing expertise is expected to have major impact in research and development of UWB systems, emphasis is placed on the DSP aspects.