Plants of the Passiflora genus are widely cultivated for the production of fruit, cosmetics and pharmacological products and for floriculture. Here, we review the history of the identification of viral pathogens involved in passion fruit woodiness disease, which can affect different species of Passiflora. Additionally, we discuss prospects for research and development related to this pathosystem and applications to plant breeding. We discuss the different potyviruses identified as potential causal agents of passion fruit woodiness in Africa, Asia, Australia and Brazil. We focus on the status of the cultivation of different Passiflora species in Brazil and place this problem in a global context. Both classical and molecular strategies for obtaining virus-resistant Passiflora plants are discussed in this work, thus providing insight into this pathosystem and useful information for breeders of Passiflora species.