One of the features of 5G wireless communication systems is to offer
wireless communication with extremely high reliability guarantees,
also known as Ultra-Reliable Communication (URC).
The level of reliability, going sometimes down to packet error rates (PER)
of $10^{-8}$, should be sufficiently convincing in order to remove
cables in an industrial setting, remote control of robots and drones
that need to perform a critical function, remote surgery or self-driving
cars. In this talk we will present elements from physical and statistical modeling of the wireless channel that are relevant for characterization of the lower
tail of the channel Cumulative Distribution Function (CDF). Specifically, we show that the use of two-wave model leads to pessimistic predictions of the fading in the region of ultra-reliable communications, while the CDFs of models that contain diffuse components have slopes that correspond to the slope of a Rayleigh fading.