The Delta and Kappa variants of SARS-CoV-2 co-emerged in India in late 2020, with the Delta variant underlying the resurgence of COVID-19, even in countries with high vaccination rates. In this study, we assess structural and biochemical aspects of viral fitness for these two variants using cryo-electron microscopy (cryo-EM), ACE2-binding and antibody neutralization analyses. Both variants demonstrate escape of antibodies targeting the N-terminal domain, an important immune hotspot for neutralizing epitopes. Compared to wild-type and Kappa lineages, Delta variant spike proteins show modest increase in ACE2 affinity, likely due to enhanced electrostatic complementarity at the RBD-ACE2 interface, which we characterize by cryo-EM. Unexpectedly, Kappa variant spike trimers form a novel head-to-head dimer-of-trimers assembly, which we demonstrate is a result of the E484Q mutation. The combination of increased antibody escape and enhanced ACE2 binding provides an explanation, in part, for the rapid global dominance of the Delta variant.