Functional polyolefins (i.e., polyethene or polypropene bearing functional groups) are highly desired materials, due to their beneficial surface properties. Many different pathways exist for the synthesis of these materials, each with its own advantages and drawbacks. This review focuses on those synthetic pathways that build up a polymer chain from ethene/propene and functionalised polar vinyl monomers. Despite many recent advances in the various fields of olefin polymerisation, it still remains a challenge to synthesise high molecular-weight copolymers with tuneable amounts of functional groups, preferably with consecutive insertions of polar monomers occurring in a stereoselective way. To overcome some of these challenges, polymerisation of alternative functionalised monomers is explored as well.