Depends on the control type, but the max range is theoretically unlimited.
In the early start of things you had gas engines and a line that went the the usually wooden plane. This was called control line, and your control range was limited to the length of the line.
In the more modern world we use RF to control our UAVs, longer distances are best gained by lower frequencies which usually cost more for equipment. Followed by sensitivity of your receiver/antenna, and the output power of your signal. For doubling power output you generally use 2.3* more wattage, and increase your range by a third.
Generally your basic, cheaper setups will used 2.4gHz and get around 300 meters (~1000 feet), but this depends on other factors like interference and environment. If you use ultra-low frequencies you can penetrate miles or rock like radio equipment used in mining operations.
NASA uses the DSN (Deep Space Network), which is a system of antennas. Most deep space satellites use S-band or X-band. Their frequencies that are around of 2 GHz to 10 GHz. However newer stuff is starting to use the Ka band.
If you have LOS with the craft you can even use laser and tracker systems for very long ranges with the ability to provide a lot of data.
If you live in the US then laws regarding RC can be found here, however this is not too big of a deal as most hobbyist and companies break minor laws regarding RC unknowingly with no repercussions from the FAA.
How far can you fly a drone