Although thousands of exoplanets have been discovered, only a small fraction have been studied in detail. By spatially resolving planets from their host stars, we can directly characterize them as individual worlds. I will discuss two novel techniques to study directly imaged exoplanets in unprecedented detail: high-dispersion coronagraphy and long-baseline interferometry. With high-dispersion coronagraphy, we can study exoplanet atmospheres in extreme spectral detail, allowing us to measure molecular abundances, planetary radial velocities, and planetary spins. Long-baseline interferometry with VLTI gives us the spatial resolution of a 140 m telescope, enabling the position of exoplanets to be measured with 10-100x better precision, sub-au resolution of circumplanetary disks, and the first direct detection of a radial-velocity discovered exoplanet. I will present recent science results with both techniques and discuss their future prospects.