This talk will discuss two results on étale fundamental groups of varieties over an algebraically closed field of characteristic p>0, based on joint work with Hélène Esnault and other coauthors. The first, along with Mark Schusterman, is that the tame fundamental group is finitely presented for such a variety which is the complement of an SNC divisor in a smooth projective variety. The second, along with Jakob Stix, is to give an obstruction for a smooth projective variety to admit a lifting to characteristic 0, in terms of the structure of its étale fundamental group as a profinite group.