The purpose of this paper is to bestow the reader with a timely study of UAV cellular communications, bridging the gap between the 3GPP standardization status quo and the more forward-looking research. Special emphasis is placed on the downlink command and control (C&C) channel to aerial users, whose reliability is deemed of paramount technological importance for the commercial success of UAV cellular communications. Through a realistic side-by-side comparison of two network deployments - a present-day cellular infrastructure versus a next-generation massive MIMO system - a plurality of key facts are cast light upon, with the three main ones summarized as follows: 1) UAV cell selection is essentially driven by the secondary lobes of a base station's radiation pattern, causing UAVs to associate to far-flung cells; 2) over a 10 MHz bandwidth, and for UAV heights of up to 300 m, massive MIMO networks can support 100 kbps C&C channels in 74% of the cases when the uplink pilots for channel estimation are reused among base station sites, and in 96% of the cases without pilot reuse across the network; and 3) supporting UAV C&C channels can considerably affect the performance of ground users on account of severe pilot contamination, unless suitable power control policies are in place.