The concept of pattern within a combinatorial structure is an essential notion in combinatorics, whose study has had many developments in various branches of discrete mathematics. Among them, the research on permutation patterns and pattern-avoiding permutations has become very active. Nowadays, these researches have being developed in several other directions, one of them concerning the definition and the study of an analogue concept in other combinatorial objects. Some recent studies are presented here, concerning patterns in bidimensional structure, and, specifically, inside polyominoes. After introducing polyomino classes, I present an original way of characterizing them by avoidance constraints (namely, with excluded submatrices) and I discuss how canonical such a description by submatrix-avoidance can be. I also provide some examples of polyomino classes defined by submatrix-avoidance, and I conclude with some hints for future research on the topic.