Totipotency is the ability of a single cell to give rise to all of the differentiated cell types that build the conceptus, yet how to capture this property in vitro remains incompletely understood. Defining totipotency relies on a variety of assays of variable stringency. Here, we describe criteria to define totipotency. We explain how distinct criteria of increasing stringency can be used to judge totipotency by evaluating candidate totipotent cell types in mice, including early blastomeres and expanded or extended pluripotent stem cells. Our data challenge the notion that expanded or extended pluripotent states harbour increased totipotent potential relative to conventional embryonic stem cells under in vitro and in vivo conditions.