It is well-known that the p-Hardy inequality is valid in a domain if the complement of the domain is uniformly p-fat. The same is true for the so-called pointwise Hardy inequalities as well, but for these the uniform fatness of the complement is also necessary, and so there is an equivalence between the two concepts. I will discuss this result and related Hausdorff content density conditions, and also some generalizations for weighted Hardy inequalities.