Laser-induced optical breakdown by femtosecond pulses is extraordinarily precise when the energy is near threshold. Despite numerous applications, the basis for this deterministic nature has not been determined. We present experiments that shed light on the basic mechanisms of light-matter interactions in this regime, which we term ''optics at critical intensity.'' We find that the remarkably sharp threshold for laser-induced material damage enables the structure or properties of materials to be modified with nanometer precision. Through detailed study of the minimum ablation size and the effects of polarization, we propose a fundamental framework for describing light-matter interactions in this regime. In surprising contrast to accepted damage theory, multiphoton ionization does not play a significant role. Our results also reject the use of the Keldysh parameter in predicting the role of multiphoton effects. We find that the dominant mechanism is Zener ionization followed by a combination of Zener and Zenerseeded avalanche ionization. We predict that the minimum feature size ultimately depends on the valence electron density, which is sufficiently high and uniform, to confer deterministic behavior on the damage threshold even at the nanoscale. This behavior enables nanomachining with high precision, which we demonstrate by machining highly reproducible nanometer-sized holes and grooves in dielectrics.