These come in three main varieties:
In these the deck is swung sideways from one bank, or even an island in the middle of the water.

The photograph above shows a typical hand operated swing bridge allowing vehicles to cross the Leeds Liverpool Canal to drive along a farm track.

The second photograph shows a more modern swing bridge carrying a road over the marina entrance at Preston.
In these the deck is hinged at one bank, and raised at the other. These are again quite common on canals (especially in Amsterdam) because they can be operated by hand if the deck has a counterweight.

A much grander version of this type of bridge, where there are two decks which rise, is London's Tower Bridge.
These are not very common. There is only one working example remaining in England (and that was closed for repair on the day I visited to photograph it).
The photograph shows the bridge across the River Tees at Middlesborough. In a transporter bridge, the deck is a movable platform, suspended from an overhead framework which spans the water. The diagram below shows this more clearly than the photograph.
Can list the advantages and disadvantages of each type of movable bridge?
Moveable bridges on all main roads have either been replaced by high level bridges, or they rarely need to be moved because of the decrease in river/canal traffic.