In 2013 Arthur characterized local Arthur packets, and, in doing so, defined a class of irreducible admissible representations of p-adic groups that contains irreducible tempered representations but is still manageably small compared to the class of all irreducible admissible representations: a representation is of Arthur-type if it is contained in an Arthur packet. In this talk I will discuss representations of Arthur type of p-adic groups in terms of singularities appearing in the stack of local Langlands parameters, highlighting open questions about these representations.