The presence of an electrical transport current in a material is one of the simplest and most important realizations of nonequilibrium physics. The current density breaks the crystalline symmetry and can give rise to dramatic phenomena, such as sliding charge density waves, insulator-to-metal transitions, or gap openings in topologically protected states. Almost nothing is known about how a current influences the electron spectral function, which characterizes most of the solid's electronic, optical, and chemical properties. Here we show that angle-resolved photoemission spectroscopy with a nanoscale light spot provides not only a wealth of information on local equilibrium properties, but also opens the possibility to access the local nonequilibrium spectral function in the presence of a transport current. Unifying spectroscopic and transport measurements in this way allows simultaneous noninvasive local measurements of the composition, structure, many-body effects, and carrier mobility in the presence of high current densities. In the particular case of our graphene-based device, we are able to correlate the presence of structural defects with locally reduced carrier lifetimes in the spectral function and a locally reduced mobility with a spatial resolution of 500 nm.