  Softer than soft, squishy granular matter is composed of grains capable of
significantly changing their shape (typically larger than 10% of deformation)
without tearing or breaking. Because of the difficulty to test these materials
experimentally and numerically, such a family of discrete systems remains
largely ignored in the granular matter physics field despite being commonly
found in nature and industry. Either from a numerical, experimental, or
analytical point of view, the study of highly deformable granular matter
involves several challenges covering, for instance: ($i$) the need to include a
large diversity of grain rheology, ($ii$) the need to consider \dc{large
material} deformations, and ($iii$) the analysis upon the effects the large
body distortion has on the global scale. In this article, we propose a thorough
definition of these squishy granular systems, and we summarize the upcoming
challenges in their study.
