Wireless communication amounts to encoding information onto physical observables carried by electromagnetic (EM) fields, radiating them into surrounding space, and detecting them remotely by an appropriate sensor connected to an informationdecoding receiver. Each observable is second order in the fields and fulfills a conservation law. In present-day radio only the EM linear momentum observable is fully exploited. A fundamental physical limitation of this observable, which represents the translational degrees of freedom of the charges (typically an oscillating current along a linear antenna) and the fields, is that it is single-mode. This means that a linear-momentum radio communication link comprising one transmitting and one receiving antenna, known as a single-input-single-output (SISO) link, can provide only one transmission channel per frequency (and polarization). In contrast, angular momentum, which represents the rotational degrees of freedom, is multi-mode, allowing an angular-momentum SISO link to accommodate an arbitrary number of independent transmission channels on one and the same frequency (and polarization). We describe the physical properties of EM angular momentum and how they can be exploited, discuss real-world experiments, and outline how the capacity of angular momentum links may be further enhanced by employing multi-port techniques, i.e., the angular momentum counterpart of linear-momentum multiple-input-multiple-output (MIMO).