There are three types of cycle carrier available and each comes with its own pros and cons.
Roof mounted Cycle Carrier
Pluses
These have performed well in independent test, primarily in terms of how well they remain attached to a car under stress conditions.
They will fit almost all cars that have a roof bar.
They don't limit the view from the rear window of the car.
Minuses
If you haven't already got them you will need to buy roof bars, around £50+.
It is generally more difficult to load and unload bikes, as you'll have to lift the cycle onto and off the roof, this risks scratching the car.
The extra height added to the vehicle could restrict entry to car parks, bridges and ferries with low maximum headroom.
This type of carrier generates more wind noise than rear-mounted carriers.
Tow-bar mounted Cycle carriers
Pluses
Some carriers can be tilted to allow access to the boot.
Are more secure under tough driving conditions than rear-mounted cycle carriers.
Minuses
It can be an expensive choice, especially if you also need to fit a tow bar and ball (around £200 including electrics for a trailer board).
Not all carriers are compatible with both types of tow ball, so check before you buy.
The pricier models are heavy and need a lot of space to store.
Cheaper models may obscure number plates and lights, which legally must be visible, if it doesn't come with a trailer board, you may need to buy one.
Rear mounted cycle carriers
Pluses
There is no need to buy roof bars or tow balls with these carriers.
They are generally less awkward to fit.
It is easier to load bikes on and off than a roof mount carrier.
Minuses
Accidents with rear-mounted carriers are more common than with other types, as they may restrict visibility through rear-view mirrors and have adjustable straps that need regular tightening.
They sometimes obscure number plates and lights so you may need to buy a lighting board (around £30) and an extra number plate. 'High-mount' carriers may avoid the problem, depending on the car model, but cause additional wind drag.
These types of carrier restrict access to boot.
Often car-model specific, so check that the carrier you want will fit your car.