The scanning tunneling microscope (STM) is a powerful spectroscopic probe of microscopic structures at metal surfaces. Here a series of STM studies are discussed that focus on the interaction of two-dimensional (2-d) electrons with surface nanostructures, and on the electronic properties of magnetic adsorbates. Spectroscopic imaging is shown to be a useful method for observing quantum interference patterns of 2-d surface state electrons scattering from natural and atomically fabricated surface structures. Surface state dispersion and scattering phaseshifts are extracted from such images. On Au(111) the interaction of surface state electrons with a reconstruction-induced superlattice is seen to lead to electronic density modulation and a new surface bandstructure. Local spectroscopic measurements at the gold surface are used to extract quantitative details of the superlattice potential. Magnetic scattering at cobalt atoms deposited onto Au(111) is observed to induce electronic fluctuations near the site of these impurities. Spin-dependent interaction between gold conduction electrons and a Co local moment leads to a many-body groundstate known as the Kondo effect. Local spectroscopic measurements of the ‘Kondo resonance’ for individual magnetic impurities are discussed. Atomic manipulation of Kondo impurities is combined with STM spectroscopy to study the interaction between magnetic atoms at a metal surface.