It is envisaged that 5G can enable many vehicular use cases that require high capacity, ultra-low latency and high reliability. To support this, 5G proposes the use of dense small cells technology as well as and highly directional mmWave systems deployment, among many other new advanced communication technologies, to boost the network capacity, reduce latency and provide high reliability. In such systems, enabling vehicular communication, where the nodes are highly mobile, requires robust mobility management techniques to minimise signalling cost and interruptions during frequent handovers. This presents a major challenge that communication system engineers need to address to realise the promise of 5G systems for V2X and similar applications. In this paper, we provide an overview of recent progresses in the development of handover and beam management techniques in 5G communication systems. We conduct a critical appraisal of current research on beam level and cell level mobility management in 5G mmWave networks considering the ultra-reliable and low-latency communication requirements within the context of V2X applications. We also provide an insight into the open challenges and the emerging trends as well as the possible evolution beyond the horizon of 5G.