The advent of petascale computation and the multicore revolution has enabled atomistic simulations of biological and soft-materials systems at previously unimaginable time and length scales. Such calculations offer exciting opportunities to advance fundamental understanding by explicitly modeling the microscopic details that dictate system-level properties. Attendant to this new wealth of data are new challenges in its interpretation. In particular, it remains a difficult task to resolve from the multitudinous atomic degrees of freedom, the collective dynamical mechanisms governing the stability and evolution of the system. We shall discuss our application and development of a nonlinear machine learning approach – the diffusion map – to systematically recover low-dimensional projections of system dynamics into kinetically meaningful collective variables. In analogy with the Mori-Zwanzig projection operator formalism, this embedding captures the slow subspace of the system dynamics, furnishing precisely the lumped variables that govern its long-time scale behavior and evolution. We shall describe our inference of the folding mechanism of an antimicrobial "lasso" peptide, and the self-assembly mechanisms of anisotropic patchy colloidal particles into icosahedral clusters. Finally, we will discuss how our approach offers a computational platform for the rational design of self-assembling materials that intrinsically accounts for both the thermodynamic and kinetic aspects of assembly.