Dependability is a measure of availability and reliability of systems/services. In the context of communication systems, dependability is governed by the coverage probability of the network under prescribed service requirements, by the latency of data transmissions as well as by the transmission error probability. Achieving dependable connectivity can be very challenging, especially within wireless mobile communications, where the transmission channel is often prone to severe fading and strong interference. Current generations of cellular mobile communication systems (4G and below) can mainly provide best effort services and are not well equipped to achieve a sufficiently high level of dependability as required by many novel applications, such as, road-safety relevant information exchange in vehicular communications, as well as, wireless remote operation of robots and drones. Standardization bodies have already recognized the market potential of such use-cases for mobile communications, and correspondingly efforts are ongoing to enhance the fifth generation of cellular systems (5G) towards ultra-reliable low-latency transmission. In this paper, we provide insights gained by our research work within the Christian Doppler Laboratory for Dependable Wireless Connectivity for the Society in Motion with respect to factors influencing the dependability of 5G mobile cellular systems, and we present our achievements over the past two years for enhancing the robustness, reliability and efficiency of dependable wireless communications.