Pattern containment and pattern avoidance in colored and/or circular permutations

Patterns in permutations has been an interesting topic of research for many years. In terms of pattern containment, we are interested in either a permutation, as short as possible, that contains a given collection of patterns (this permutation is called a superpattern); or the number of times some patterns can be contained in a permutation (called pattern packing). On the other hand, in pattern avoidance, we explore permutations, as long as possible, without a particular pattern or set of patterns. In this review chapter, we will review some of the recent work on pattern packing, superpatterns, and pattern avoidance when colored or circular patterns/permutations are considered.