IIRC, they are construction-only engineers, meaning they build things like airfields (their original purpose), but do not assault fortifications or the like.
In WW2, there was usually at least one CB assigned to each Marine Division or Corps.
Other engineers-- that's going to vary by army, but the usual is a battalion of combat engineers to a division. These guys can do some road clearing & repairs, build or repair bridges, and build or attack fortifications and minefields. There should be a company each for mines, bridges (may include assault boats), fortifications and roads, with the specialized equipment for each. Some brigades/regiments would have their own separate company, too, with specialized platoons for the above roles.
In some armies (German, French and Italian come to mind) there are pure combat engineer (a.k.a. sappers or pioneers) units.
Above that, there are regiments or brigades of engineers at the corps and higher levels. These are the ones for building/operating things like dams or waterways, power plants, sawmills, roads, and everything else. Airfields are often built/repaired by specialist units, which usually belong to their nation's air force. Railroad repair or operating units may be independent, or belong to the engineer branch, too.
Is that broad enough?
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My Twilight claim to fame: I ran "Allegheny Uprising" at Allegheny College, spring of 1988.
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