  This article introduces an analogue of permutation classes in the context of
polyominoes. For both permutation classes and polyomino classes, we present an
original way of characterizing them by avoidance constraints (namely, with
excluded submatrices) and we discuss how canonical such a description by
submatrix-avoidance can be. We provide numerous examples of permutation and
polyomino classes which may be defined and studied from the submatrix-avoidance
point of view, and conclude with various directions for future research on this
topic.
