Brassica juncea (L.) Czern. & Coss. (Indian mustard) is an economically important edible oil crop. Over the years, plant breeders have developed many elite varieties of B. juncea with better yield traits, but research work on the introgression of stress resilience traits has largely been lagging due to scarcity of resistant donors. Crop wild relatives (CWRs) are the weedy relatives of domesticated plant species which are left unutilized in their natural habitat due to the presence of certain undesirable alleles which hamper their yield potential, and thus, their further domestication. CWRs of B. juncea namely include Sinapis alba L. (White mustard), B. tournefortii Gouan. (African mustard), B. fruticulosa Cirillo (Twiggy turnip), Camelina sativa L. (Gold-of-pleasure), Diplotaxis tenuisiliqua Delile (Wall rocket), D. erucoides L. (White wall rocket), D. muralis L. (Annual wall rocket), Crambe abyssinica R.E.Fr. (Abyssinian mustard), Erucastrum gallicum Willd. (Common dogmustard), E. cardaminoides Webb ex Christ (Dogmustard), Capsella bursa-pastoris L. (Shepherds purse), Lepidium sativum L. (Garden Cress) etc. These CWRs have withstood several regimes of biotic and abiotic stresses over the past thousands of years which led them to accumulate many useful alleles contributing in resistance against various environmental stresses. Thus, CWRs could serve as resourceful gene pools for introgression of stress resilience traits into Indian mustard. This review summarizes research work on the introgression of resistance against Sclerotinia stem rot (caused by Sclerotinia sclerotiorum), Alternaria blight (caused by Alternaria brassicae), white rust (caused by Albugo candida), aphid attack, drought and high temperature from CWRs into B. juncea. However, various pre- and post-fertilization barriers due to different ploidy levels are major stumbling blocks in the success of such programmes, therefore, we also insightfully discuss how the advances made in -omics technology could be helpful in assisting various breeding programmes aiming at improvisation of stress resilience traits in B. juncea.