Wireless 5G systems will not only be "4G, but faster". One of the novel features discussed in relation to 5G is Ultra-Reliable Communication (URC), an operation mode not present in today's wireless systems. URC refers to provision of certain level of communication service almost 100 % of the time. Example URC applications include reliable cloud connectivity, critical connections for industrial automation and reliable wireless coordination among vehicles. This paper puts forward a systematic view on URC in 5G wireless systems. It starts by analyzing the fundamental mechanisms that constitute a wireless connection and concludes that one of the key steps towards enabling URC is revision of the methods for encoding control information (metadata) and data. It introduces the key concept of Reliable Service Composition, where a service is designed to adapt its requirements to the level of reliability that can be attained. The problem of URC is analyzed across two different dimensions. The first dimension is the type of URC problem that is defined based on the time frame used to measure the reliability of the packet transmission. Two types of URC problems are identified: long-term URC (URC-L) and short-term URC (URC-S). The second dimension is represented by the type of reliability impairment that can affect the communication reliability in a given scenario. The main objective of this paper is to create the context for defining and solving the new engineering problems posed by URC in 5G.