Big Ramsey degrees are strengthenings of ordinary Ramsey degrees. Given a coloring of the embeddings of a finite structure into a Fraisse limit, instead of searching for arbitrarily large finite structures in few colors, we search for a copy of the entire Fraisse limit in few colors. For example, considering the 2-element linear order in the class of finite linear orders, its big Ramsey degree is 2, while its ordinary Ramsey degree is 1. In recent joint work with several authors, the exact big Ramsey degrees for any structure in a finitely constrained binary free-amalgamation class are characterized. In all examples where big Ramsey degrees are fully characterized, one in fact shows the stronger result that there is a strong big Ramsey structure, an expansion of the Fraisse limit which recovers the exact big Ramsey degrees of every finite substructure and which satisfies an analog of the infinite Ramsey theorem. In joint work with Dobrinen, we strengthen this to show that these strong big Ramsey structures, here called diagonal diaries, satisfy an analog of Ellentuck's theorem about definable colorings of the infinite subsets of omega. Time permitting, we will state a conjecture in the spirit of theorems about ordinary Ramsey degrees by Zucker, Melleray - Nguyen Van The - Tsankov, and Ben Yaacov - Melleray - Tsankov.