  As white-dwarf (WD) stars cool, they go through one or more stages of
$g$(gravity)-mode pulsational instability, becoming multiperiodic variable
stars. Stars passing through these instability domains allow astronomers to
study their interiors through asteroseismological techniques, as if they could
"look" at their interiors by analyzing the spectra of pulsation periods. WD
asteroseismology has experienced extraordinary advances in recent years thanks
to photometric observations of unprecedented quality delivered by space
missions such as Kepler and TESS. These advances in the monitoring of variable
WDs have been accompanied by the development of new stellar models and
techniques for modeling their pulsations. In this article, we review the most
outstanding findings -- up to early 2022 -- about these fascinating pulsating
stars made possible with the high-sensitivity and continuous observations of
the ongoing TESS mission, bearing in mind that there will possibly be many more
new results in the immediate future derived from this unique space telescope.
