Attosecond observations of coherent electron dynamics in molecules and nanostructures can be achieved by combining conventional scanning tunneling microscopy (STM) with ultrashort femtosecond laser pulses. While experimental studies in the subcycle regime are under way, a robust strong-field theory description has remained elusive. Here we devise a model based on the strong-field approximation. Valid in all regimes, it provides a surprising analogy to the standard model of STM. We show that the intuitive three-step model of attosecond science directly emerges from our model and we also describe the optimal conditions for attosecond STM experiments.