Biotic and abiotic constraints seriously affect the productivity of agriculture worldwide. The broadly recognized benefits of legumes in cropping systems—biological nitrogen fixation, improving soil fertility and broadening cereal-based agro-ecologies, are desirable now more than ever. Legume production is affected by hostile environments, especially soil salinity and high temperatures (HTs). Among legumes, mungbean has acceptable intrinsic tolerance mechanisms, but many agro-physiological characteristics of the Vigna species remain to be explored. Mungbean has a distinct advantage of being short-duration and can grow in wide range of soils and environments (as mono or relay legume). This review focuses on salinity and HT stresses on mungbean grown as a fallow crop (mungbean-rice-wheat to replace fallow-rice-wheat) and/or a relay crop in cereal cropping systems. Salinity tolerance comprises multifaceted responses at the molecular, physiological and plant canopy levels. In HTs, adaptation of physiological and biochemical processes gradually may lead to improvement of heat tolerance in plants. At the field level, managing or manipulating cultural practices can mitigate adverse effects of salinity and HT. Greater understanding of physiological and biochemical mechanisms regulating these two stresses will contribute to an evolving profile of the genes, proteins, and metabolites responsible for mungbean survival. We focus on abiotic stresses in legumes in general and mungbean in particular, and highlight gaps that need to be bridged through future mungbean research. Recent findings largely from physiological and biochemical fronts are examined, along with a few agronomic and farm-based management strategies to mitigate stress under field conditions.