To this day, wireless communications, as well as radio astronomy and other radio science and technology applications, have made predominantly use of techniques built on top of the electromagnetic linear momentum physical layer. As a supplement and/or alternative to this conventional approach, techniques rooted in the electromagnetic angular momentum (moment of momentum) physical layer have been advocated, and promising results from proof-of-concept laboratory and real-world angular momentum wireless and fiber communication experiments were recently reported. A physical observable in its own right, albeit much more sparingly used than other electromagnetic observables such as energy and linear momentum, the angular momentum exploits the rotational symmetry of the electromagnetic field and the rotational (spinning and orbiting) dynamics of the pertinent charge and current densities. Here we present a review of the fundamental physical properties of the electromagnetic angular momentum observable, derived from the fundamental postulates of classical electrodynamics (the Maxwell-Lorentz equations), and put it into its context among the other Poincaré symmetry invariants of the electromagnetic field. The multi-mode quantized character and other physical properties that sets the classical electromagnetic angular momentum apart from the electromagnetic linear momentum are pointed out. We give many of the results both in terms of the electric and magnetic field vectors and in terms of the complex Riemann-Silberstein vector formalism (Majorana-Oppenheimer representation of classical electrodynamics) and discuss formal parallels with first quantization formalism. We introduce generalized and symmetrized extensions of the Jefimenko integral formulas for calculating exact expressions for the electric and magnetic fields directly from arbitrary given electric and/or magnetic source distributions and use them for deriving expressions for the volumetric density of the electromagnetic angular momentum radiated from any given arbitrary localized distribution of charges and currents. Our results generalize earlier results, obtained by other authors for certain specific configurations only, and facilitate the modeling and design of angular momentum transducers. They show that the volume integrated angular momentum density, i.e., the total angular momentum emitted by the sources, always tends asymptotically to a constant when the distance from the source volume tends to infinity, proving that a radiation arrow of time exists also for angular momentum, as it does for linear momentum (the volume integrated Poynting vector). Consequently, angular momentum physics (torque action) offers an alternative or a supplement to linear momentum physics (force action) as a means of transferring information wirelessly over very long distances. This finding opens possibilities for, among other things, a more flexible utilization of the radio frequency spectrum and paves the way for the development of new information transfer techniques. We discuss ...