The carbene character of carbon monoxide offers the possibility to utilize this C$_1$-building block for the carbonylation of a variety of organic substrates by insertion of CO into $\sigma$-bonds. Although presenting an ideal atom economy this route requires the design and utilization of reactive catalysts able to activate strong CO , C-N, and C-H bonds in the presence of carbon monoxide. This perspective article adresses, in the context of sustainable chemistry, the challenges and strategies facing the catalytic carbonylation of $\sigma$-bonds and presents the key advances in the field over the last decades, for the carbonylation polar and apolar substrates, such as the conversion of alcohols to formates and esters and the carbonylation of amines to amides.