DAB. There are 2 types of transmitter, the small local ones (eg Crockerton) which transmit the commercial stations and the big heavy duty ones (eg Mendip) which transmit the BBC stations and Classic fm. You may have problems without an external aerial, and depending on where you live this may not work either. More info here. Most DAB radios' telescopic aerials can be removed to facilitate connection of an external aerial. Often if a DAB radio is connected to an FM aerial (or even sometimes a tv aerial) it works fine.
FM. As you probably know, the reception is not all that great around here. Most stations are transmitted from either The Isle of Wight or Wenvoe (South Wales). Yes, we are on the fringe of both! There is a network of local repeaters and small transmitters for local stations (eg 3tr fm).
FM and DAB external aerials. These come in 2 flavours, omnidirectional and directional. Omnidirectional have lower performance but receive from any transmitter in range. Directional aerials have better performance but only really work for the transmitter they are pointing at. If you are after hiss free reception then I reccommend a directional aerial. My house is reasonably high, I use an omnidirectional aerial and can hear very slight hissing, more noticeable on stations like Radio 4 and Classic fm. Radio and tv signals can easily be combined to go down one cable.
FM aerials do in fact work to a lesser degree for DAB and vice versa.
Internet. Most radio stations can be picked up by a PC hooked up to broadband.
Freeview/freesat/sky. These services provide most radio stations. Only problem is that you need the television on! Some integrated TV's have a "radio mode"
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