Over the last few decades, the world has witnessed radical changes in climate, landscape, and ecosystems. These events, together with other factors such as increasing illegal wildlife trade and changing human behaviour towards wildlife, are resulting into thinning boundaries between wild canids and felids and their domestic counterparts. As a consequence, the epidemiology of diseases caused by a number of infectious agents is undergoing profound readjustements, as pathogens adapt to new hosts and environments. Therefore, there is a risk for diseases of wildlife to spread to domestic carnivores and vice versa, and for zoonotic agents to emerge or re-emerge in human populations. Hence, the identification of the hazards arising from the co-habitation of these species is critical in order to plan and develop adequate control strategies against these pathogens. In the first of this two-part article, we review the role that wild canids and felids may play in the transmission of protozoa and arthropod-borne agents to dogs and cats in Europe, and provide an account of how current and future progress in our understanding of the ecology and epidemiology of parasites, as well as of host-parasite interactions, can assist efforts aimed at controlling parasite transmission.