In this paper I am interested in Aristotelian essentialism only as it relates to Aristotle's notion of an ordinary object. In particular, I shall concentrate on two main kinds of interpretation that are to be distinguished here. First, there is what I call the standard version. So named because it formulates the preferred view among commentators, the standard version holds that essences are necessary (at least) for the existence of objects. Against this is a recently proposed line of interpretation which I shall call the non-standard version of Aristotelian essentialism. It holds that possessing a given essential property is only sufficient, not necessary, for the existence of a given object and so denies the standard version. While I focus mainly on arguments and evidence that bear on decision between the two versions, I also reflect some on whether Aristotle is best construed a de re or a de dicto essentialist. Part I of the paper spells out the versions in question. Part II contains considerations which show Aristotle's openness to de re essentialism.