Supported bimetallic nanoparticulate catalysts are an important class of heterogeneous catalysts for many reactions including selective oxidation, hydrogenation/hydrogenolysis, reforming, biomass conversion reactions and many more. The activity, selectivity and stability of these catalysts depend on their structural features including particle size, composition and morphology. In this review, we present important structural features relevant to supported bimetallic catalysts focusing on Pd-based bimetallic systems and recently reported strategies to control them through different synthesis methodologies. Further, we focus on a few reactions that are relevant to environmental catalysis i.e. (a) CO oxidation, (b) hydrocarbon oxidation, (c) hydrodechlorination and (d) NOx decomposition where Pd-based catalysts are often used successfully. In spite of much progress in these areas, still there is a need for more advanced catalytic technologies to address the grand challenges like environmental remediation. Some of the recent advances in the design of bimetallic catalysts were made because of the combined efforts of material scientists, spectroscopists, microscopists, catalysis chemists and engineers through state-of-the-art characterisation methodologies, mechanistic investigations and structure-activity correlations. This review is aimed at inspiring scientists to rationally design catalysts for a green and sustainable future.