Maglev
The world's first commercial maglev system was a low-speed maglev shuttle that ran between the airport terminal of Birmingham International Airport and the nearby Birmingham International railway station between 1984 and 1995. Its track length was , and trains levitated at an altitude of , levitated by electromagnets, and propelled with linear induction motors. It operated for 11 years and was initially very popular with passengers, but obsolescence problems with the electronic systems made it progressively unreliable as years passed, leading to its closure in 1995. One of the original cars is now on display at Railworld in Peterborough, together with the RTV31 hover train vehicle. Another is on display at the National Railway Museum in York.
Monorail
Magnetic levitation train (maglev) systems by the German Transrapid were built as straddle-type monorails, as they are highly stable and allow rapid deceleration from great speed. At speed, maglev trains hover over the track and are not in physical contact with it. The maglev is the fastest train of any type, the experimental SCMaglev having recorded a speed of . The commercial Shanghai Maglev Train has run at . However, the guideway is so wide that it can be argued it is not legitimate to call it a monorail. 
There are also slower maglev monorails intended for urban transport, such as Japan's Linimo (2003).