The Fano effect is ubiquitous in the spectroscopy of, for instance, atoms, bulk solids and semiconductor heterostructures. It arises when quantum interference takes place between two competing optical pathways, one connecting the energy ground state and an excited discrete state, the other connecting the ground state with a continuum of energy states. The nature of the interference changes rapidly as a function of energy, giving rise to characteristically asymmetric lineshapes. The Fano effect is particularly important in the interpretation of electronic transport and optical spectra in semiconductors. Whereas Fano's original theory applies to the linear regime at low power, at higher power a laser field strongly admixes the states and the physics becomes rich, leading, for example, to a remarkable interplay of coherent nonlinear transitions. Despite the general importance of Fano physics, this nonlinear regime has received very little attention experimentally, presumably because the classic autoionization processes, the original test-bed of Fano's ideas, occur in an inconvenient spectral region, the deep ultraviolet. Here we report experiments that access the nonlinear Fano regime by using semiconductor quantum dots, which allow both the continuum states to be engineered and the energies to be rescaled to the near infrared. We measure the absorption cross-section of a single quantum dot and discover clear Fano resonances that we can tune with the device design or even in situ with a voltage bias. In parallel, we develop a nonlinear theory applicable to solid-state systems with fast relaxation of carriers. In the nonlinear regime, the visibility of the Fano quantum interferences increases dramatically, affording a sensitive probe of continuum coupling. This could be a unique method to detect weak couplings of a two-level quantum system (qubits), which should ideally be decoupled from all other states.