Rivers have been introduced in OpenTTD during the development towards OpenTTD 0.6.0 (more specifically in r11926). The first testing release which contained the feature was OpenTTD 0.6.0-beta 4. Rivers are similar to canals but can be generated during the map generation process (since r22767). Players can only build river in the scenario editor (available in the waterways construction menu) but not in normal gameplay. Canals function in a similar way, with the only difference being that rivers can be created on a straight slope (but not diagonal slope).
Ships can sail via level river, but the river on a slope must be rebuilt into a lock for passage. Rivers will automatically connect to other river and canal tiles when they are constructed adjacent to each other. Docks can be constructed on the river, given that there are enough River or Canal tiles and a straight slope against the level river tile. Buoys can be placed on a level river tile without a problem too.
In normal gameplay, a player can demolish the river tile and restore it to normal land. The cost of demolishing a river tile is the same as demolishing a sea-level water tile with the base cost of £7,500 ($15,000) per tile. (On a side note, this is twice the cost of constructing Canal over the River as well as demolishing the Canal.) Unlike trees or buildings owned by towns, demolishing river does not reduce a company's rating to the nearby Local authority. Towns will not demolish rivers while extending; instead, it will use Bridges to cross over the river.