Architectured materials exhibit unconventional properties directly linked to their geometry. When composed of slender elements, architectured materials can undergo large deformations exhibiting geometric non-linearities through buckling or snapping behaviours of the cell walls. This can create a new pattern in the material with different properties than the original structure. In this article, we present a review of methods for studying pattern generating architectured materials caused by elastic instabilities. We start by reviewing the relevant studies on a classical example : hexagonal honeycombs under compression. We highlight their importance in identifying the underlying bifurcation phenomenon and their contributions to the elaboration of methods for studying mesoscopic (unit-cell length) pattern changes in architectured materials. We then exhaustively review the methods and tools used up to now to study the post-bifurcated behaviour of such materials subject to elastic instabilities.