We describe the results of a study at atomic resolution of the structures exhibited by polymer-capped monometallic and bimetallic Pt and Pd- nanoclusters-models for nanoscale material electrocatalysts -as carried out using an aberration-corrected scanning transmission electron microscope (STEM). The coupling of sub-nanometer resolution with Z-contrast measurements provides unprecedented insights into the atomic structures and relative elemental speciation of Pt and Pd within these clusters. The work further defines the nature of deeply quenched states that prevent facile conversions of core-shell motifs to equilibrium alloys and the nature of nonidealities such as twinning (icosahedral cores) and atomic segregation that these structures can embed. The nature of the facet structure present in these model systems is revealed by theory directed modeling in which experimental intensity profiles obtained in Z-contrast measurements at atomic resolution are compared to simulated intensity profiles using theoretically predicted cluster geometries. These comparisons show close correspondences between experiment and model and highlight striking structural complexities in these systems that are compositionally sensitive and subject to amplification by subsequent cluster growth processes. The work demonstrates an empowering competency in nanomaterials research for STEM measurements carried out using aberration corrected microscopes, approaches that hold considerable promise for characterizing the structure of these and other important catalytic materials systems at the atomic scale.