T waves propagate in the so-called SOFAR channel of minimum sound velocity acting as a waveguide for acoustic energy in the world's oceans. They can be excited by sources in the solid Earth such as earthquakes through conversion of seismic energy into acoustic waves at the solid-liquid interfaces. We present a historical perspective of the investigations of such conversions. In the context of geometrical optics, a sloping interface provides a mechanism for the penetration of the SOFAR channel after a series of reflections in the liquid wedge. This process, known as "downslope conversion", successfully explained many characteristics of earthquake-generated T waves, but has severe limitations, notably regarding "abyssal" T phases, generated under flat oceanic basins. We review theoretical developments based on mode theory which describe coupling between elastic and acoustic modes under scattering by structural heterogeneities located at the ocean bottom, and which are becoming increasingly successful at modeling the waveshapes of abyssal T phases. As a particular form of seismic wave emanating from an earthquake, T waves can provide insight into seismic sources in the oceanic environment. We review the application of T waves to the detection of small earthquakes in marine basins, discuss the retrieval of seismic source properties from T-phase waveforms, and show that several algorithms combining measurements of their amplitude and duration can yield information on source rupture, and more specifically detect the presence of source slowness. In particular, anomalously slow earthquakes such as the so-called "tsunami earthquakes" are poor T-wave generators, and more generally, T-phase amplitudes and tsunami generation are not found to correlate. In the context of the Comprehensive Nuclear-Test Ban Treaty, hydroacoustics has been recognized as a monitoring technology, and the deployment of state-of-the-art receivers at eleven sites will significantly improve long-range detection capabilities and open up new opportunities for the investigation of acoustic sources, including earthquakes, in the oceanic environment.