The radio band is known to be rich in variable and transient sources, but exploration of it has only begun only in the last few years. Relevant time scales are as small as a fraction of a nanosecond (giant pulses from the Crab pulsar). Short transients (less than one second, say) have signal structure in the time-frequency plane at the very least because of interstellar plasma propagation effects (dispersion and scattering), and in some cases due to emission structure. Optimal detection requires handling a range of signal types in the time-frequency plane. Short bursts by necessity have very large effective radiation brightness temperatures associated with coherent emission processes. This paper surveys relevant source classes and summarizes propagation effects that must be considered to optimize detection in large-scale surveys. Scattering horizons for the interstellar and intergalactic media are defined, and the role of the radio band in panchromatic and multimessenger studies is discussed.