Logistics is an important driver for the competitiveness of industries and material supply. The development of smart logistics, powered by precise positioning and communication technologies can significantly improve the efficiency of logistics. The emerging technology of ultra-wideband (UWB) precision positioning has attracted significant attention throughout the previous decade owing to its promising capabilities over other radio frequency-based indoor localisation systems. In addition, UWB is characterised by large bandwidth and data rate, short message length, low transmission power and high penetration capability, which are all favourable for indoor positioning applications. However, UWB localisation technology faces several challenges that are somewhat similar to other technologies, such as mitigating errors that originate from non-line-of-sight (NLOS) situations and tackling signal interference in dense environments, and when required to operate in extreme conditions. This paper reviews the most recent advances made in UWB positioning systems over the last five years, with a focus on high-ranking articles. In addition to going through more conventional solutions to UWB challenges, modern solutions, which involve the use of machine learning and sensor data fusion, are discussed. We highlight the most promising findings of the recently implemented and foreseen UWB positioning systems by providing a summary of each reviewed article. Additionally, we address a major challenge that faces the UWB positioning technology: NLOS situations, focusing on some proposed remedies such as multi-sensor fusion and machine learning. As an application, this study introduces how UWB technology promotes smart logistics by offering indoor positioning to improve efficiencies in the delivery of goods from the source to the customer. Furthermore, it demonstrates the benefits of UWB technology for accurate positioning and tracking of both stationary and moving items, and machinery in an indoor logistics environment.