I'd recommend the following two books. In the first one there are some connections to toric varieties. (Chapter 9.3: Lattice polytopes and unimodular triangulations; also they deal with regular aka coherent triangulations.)
De Loera, Jesús A.; Rambau, Jörg; Santos, Francisco, Triangulations. Structures for algorithms and applications, Algorithms and Computation in Mathematics 25. Berlin: Springer (ISBN 978-3-642-12970-4/hbk; 978-3-642-12971-1/ebook). xiii, 535 p. (2010). ZBL1207.52002.
Aurenhammer, Franz; Klein, Rolf; Lee, Der-Tsai, Voronoi diagrams and Delaunay triangulations, Hackensack, NJ: World Scientific (ISBN 978-981-4447-63-8/hbk). viii, 337 p. (2013). ZBL1295.52001.