The valleys through which these flowed were ideally suited for man-made dams that could be used to to power water mills.
A walk along the Rivelin Valley from Malin Bridge tram stop or along the Porter Valley out from Endcliffe Park towards the Peak District will reveal some of these old dams.
Bold housing projects such as the world famous (and now listed) Park Hill made Sheffield famous for the feverish vision with which architects and planners sought to reshape the city in the second half of the twentieth century.
However, the economic recession of the 1980s hit Sheffield hard, and large numbers of workers were left unemployed by the changing shape of heavy industry in Britain.
The combination of the resilient spirit of Sheffield people in these bleak times made the city famous in the black comedy 'The Full Monty', which was set and filmed in and around Sheffield.
Grand visions have routinely been proposed or initiated by the city or county councils, and European funding has been used on a number of public infrastructure projects that have shaped the city.
This is nothing new, however, since many would argue that post-war town planners did more damage to the face of Sheffield than the Luftwaffe did during the heavy nights of World War II aerial bombing.
The city centre lies where these rivers and valleys meet.
The city has expanded out along the valleys and over the hills between, creating leafy neighbourhoods and suburbs within easy reach of the city centre.
Even when making a simple purchase in a store or market, you can expect to be called 'love' at least once.
Sheffield is adapting as it becomes a more confident post-industrial city.
The crucible technique of making exceptionally high quality steel was invented here by Benjamin Huntsman in 1852, and for decades it was to give Sheffield the economic advantage over other steel producing cities.