Given an algebraic variety X and a resolution of singularities Z of X with exceptional set E it is a natural (old) question whether, or under which additional assumptions, regular differential forms defined on the smooth part of X extend over E to regular differential forms on Z. After discussing examples showing that extension is not possible in general, I will introduce and discuss (log-)canonical singularities and sketch the proof of the following result: extension (with logarithmic poles) holds for surfaces and threefolds with (log-)canonical singularities. This is joint work with Stefan Kebekus and Sándor Kovács.