IIRC there isn't a problem for most of the flight; but right as you're ascending/descending your phone can end up getting a very weak line-of-sight connection to a whole bunch of cell towers at once, which causes a few different problems, but all of which come down to "it makes both your phone, and all the towers, shout really loudly at one-another to try to achieve a circuit." Which, sure, means that there might be EM interference (on bands ATC doesn't even use, but which the pilots might like to switch to in event of emergency.)

But, more importantly, it puts your phone's radio through an unusual high-power-draw situation that the phone's manufacturer may not have bothered testing for, which can make phone batteries explode that might not have otherwise ever exploded.

Oh, and also, a plane-load of people whose phones are all ranging hogs circuits on a bunch of towers at once (for no productive purpose, since the phones don't have high-enough SNR to actually communicate anything useful with any of the towers they can "see"), so the cellular service providers have politely asked the FAA to get people to not do that.