Most of the recent advances in the design of high-speed wireless systems are based on information-theoretic principles that demonstrate how to efficiently transmit long data packets. However, the upcoming wireless systems, notably the 5G system, will need to support novel traffic types that use short packets. For example, short packets represent the most common form of traffic generated by sensors and other devices involved in Machine-to-Machine (M2M) communications. Furthermore, there are emerging applications in which small packets are expected to carry critical information that should be received with low latency and ultra-high reliability. Current wireless systems are not designed to support short-packet transmissions. For example, the design of current systems relies on the assumption that the metadata (control information) is of negligible size compared to the actual information payload. Hence, transmitting metadata using heuristic methods does not affect the overall system performance. However, when the packets are short, metadata may be of the same size as the payload, and the conventional methods to transmit it may be highly suboptimal. In this article, we review recent advances in information theory, which provide the theoretical principles that govern the transmission of short packets. We then apply these principles to three exemplary scenarios (the two-way channel, the downlink broadcast channel, and the uplink random access channel), thereby illustrating how the transmission of control information can be optimized when the packets are short. The insights brought by these examples suggest that new principles are needed for the design of wireless protocols supporting short packets. These principles will have a direct impact on the system design.