This talk will be about recent work of A. Schmidt concerning a generalization of the notion of a tame cover of an arithmetic scheme. Schmidt's generalization is relative to a compactification of the given scheme in which the boundary may not be a divisor with normal crossings. It is not known if the associated tame fundamental group is independent of the choice of compactification. But Schmidt can show that the associated pro-nilpotent tame fundamental group is independent of this choice. He also proves that the absolute tame abelian fundamental group over a given base is finite.