This is a brief review of various topological dualities for distributive lattices. In essence, Stone duality provides a categorical equivalence between bounded distributive lattices and certain compact \(T_0\) spaces [see \textit{G. Grätzer}, ``Lattice theory''. Freeman and Co., San Francisco (1971; Zbl 0232.06001) for a full characterization]. The underlying set for the Stone space is the set of prime filters of the lattice. By making the basic open sets clopen, one obtains Priestley's duality. The advantage is that the space now is Hausdorff. The great disadvantage of Priestley's duality is that a characterization of Priestley spaces hinges on an order characterization of prime filters of distributive lattices. Such a characterization is still unknown. One can also arrive at Priestley duality through the booleanization of a distributive lattice. This has been done by \textit{A. Nerode}, [Duke Math. J. 26, 397-406 (1953; Zbl 0114.24702)]. The book by \textit{R. Balbes, P. Dwinger}, ``Distributive lattices'' (1974; Zbl 0321.06012) contains a full treatment of Stone duality taking into account the substantial contributions of Nerode. The author presents Stone duality in the context of the natural Galois connection \(d \in P\) that holds between the lattice \(\mathbf D\) and the set \(\mathcal P\) of its prime filters. This approach leads to a hull-kernel topology on \(\mathcal P\) and to Cornish's approach to Priestley duality. The author puts together these various ideas on the very limited space of only five pages. The bibliography is quite complete. The paper might be useful for readers with limited knowledge of distributive lattices but with an otherwise good background in pointset topology and universal algebra.