We show that the external control of Fano resonances in general leads to complex Fano q parameters. Fano line shapes of photoelectron and transient absorption spectra in the presence of an infrared control field are investigated. Computed transient absorption spectra are compared with a model proposed for a recent experiment [C. Ott et al., Science 340, 716 (2013)]. Control mechanisms for photoelectron spectra are exposed: control pulses applied during excitation modify the line shapes by momentum boosts of the continuum electrons. Pulses arriving after excitation generate interference fringes due to infrared two-photon transitions.