Under the Whyte notation for the classification of steam locomotives0-4-0 represents one of the simplest possible types, that with two axles and four coupled wheels, all of which are driven. In normal circumstances, the wheels on each end of the axles are connected with coupling rods to form a single driven set.

In Britain the Whyte notation of wheel arrangement was also often used for the classification of electric and diesel-electric locomotives with side-rod coupled driving wheels.

0-4-0 locomotives were built as tank locomotives as well as tender locomotives. The former was more common in Europe and the latter in the United States, except in the tightest of situations such as that of a shop switcher where overall length was a concern.

The terms four-wheeled and four-coupled are often used for 0-4-0 locomotives, but these terms can also encompass other wheel arrangements. For example, Stephenson's Rocket was an 0-2-2 four-wheeled locomotive.

A four-wheeled configuration, where all the wheels are driving wheels, uses all the locomotive's mass for traction but is inherently unstable at speed. The type was therefore mainly used for switchers (USA) and shunters (UK). Because of the lack of stability, tender engines of this type were only built for a few decades in the UK. They were built for a longer period in the USA.

The possible tractive effort of an 0-4-0 within normal axle load limits was not enough to move large loads. By 1900 they had therefore largely been superseded for most purposes by locomotives with more complex wheel arrangements. They nevertheless continued to be used in situations where tighter radius curves existed or the shorter length was an advantage. Thus they were commonly employed in dockyard work, industrial tramways, or as shop switchers.

0-4-0T tank engines were introduced in the early 1850s. The type was found to be so useful in many locations that they continued to be built for more than a century and existed until the end of the steam era.

 The wheel arrangement is also used on specialised types such as fireless locomotivescrane tankstram engines and geared steam locomotives. It was also widely used on narrow gauge railways.

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