We analyze properties of electromagnetic radiation in helical undulators with a particular emphasis on the orbital angular momentum of the radiated photons. We demonstrate that all harmonics higher than the first one radiated in a helical undulator carry an orbital angular momentum. We discuss some possible applications of this phenomenon and the ways of effective generation of these photons in a helical undulator. We call for review of results of experiments performed where the higher harmonics radiated in a helical undulator might be involved.