Gene editing has the potential to make new crop varieties faster and more efficiently. New and more suitable crop varieties can increase sustainable agriculture, for instance, in the form of disease-resistant varieties that facilitate integrated pest management. The European Commission's proposal on the regulation of gene-edited and cisgenic plants produced with New Genomic Techniques (including CRISPR/Cas) has re-opened the discussion on Intellectual Property Rights on plants in Europe. We provide an overview of the possible impact of patent rights and Plant Variety Rights on the availability of technology and gene-edited alleles to breeders on an European level. We highlight potential problems with the two Intellectual Property Right systems and indicate potential avenues to solutions.