Tsunamis generate internal gravity waves (IGWs) that propagate vertically into the atmosphere and can create detectable signatures in the ionosphere. These signatures have consistently been observed in the presence of a tsunami for over a decade in the total electron content and for over 5 years in the 630.0 nm airglow. Here, we provide a comprehensive overview on the utilization of airglow imaging systems for monitoring tsunamis. We develop the basic theory behind tsunami-ionospheric coupling from first principles and give special attention to the topic of tsunami-ionospheric coupling efficiency. This is followed by the presentation and analysis of a methodology for extracting wave parameters of tsunami-induced signatures appearing in airglow images. The methodology is applied to the 11 March 2011 Tohoku and 16 September 2015 Chile tsunamis as case studies. A previously developed geometric model that takes into account the assumed posture of tsunami-induced IGWs in the geomagnetic field and the observation geometry is shown to predict the region of the sky in which the observations were seen.