Climate change will have major impacts on crop production: not just increasing drought and heat stress, but also increasing insect and disease loads and the chance of extreme weather events and further adverse conditions. Often, wild relatives show increased tolerances to biotic and abiotic stresses, due to reduced stringency of selection for yield and yield-related traits under optimum conditions. One possible strategy to improve resilience in our modern-day crop cultivars is to utilize wild relative germplasm in breeding, and attempt to introgress genetic factors contributing to greater environmental tolerances from these wild relatives into elite crop types. However, this approach can be difficult, as it relies on factors such as ease of hybridization and genetic distance between the source and target, crossover frequencies and distributions in the hybrid, and ability to select for desirable introgressions while minimizing linkage drag. In this review, we outline the possible effects that climate change may have on crop production, introduce the Brassica crop species and their wild relatives, and provide an index of useful traits that are known to be present in each of these species that may be exploitable through interspecific hybridization-based approaches. Subsequently, we outline how introgression breeding works, what factors affect the success of this approach, and how this approach can be optimized so as to increase the chance of recovering the desired introgression lines. Our review provides a working guide to the use of wild relatives and related crop germplasm to improve biotic and abiotic resistances in Brassica crop species.