  Teleparallel geometry offers a platform on which to build up theories of
gravity where torsion rather than curvature mediates gravitational interaction.
The teleparallel analogue of Horndeski gravity is an approach to teleparallel
geometry where scalar-tensor theories are considered in this torsional
framework. Being teleparallel gravity of lower order in dynamics, this turns
out to be more general than metric Horndeski gravity. In other words, the class
of teleparallel Horndeski gravity models is much broader than the standard
metric one. In this work, we explore constraints on this wide range of models
coming from ghost and Laplacian instabilities. The aim is to limit pathological
branches of the theory by fundamental considerations. It is possible to
conclude that a very large class of models results physically viable.
