In this talk I will outline recent developments in logarithmic Gromov-Witten theory, a variant of relative Gromov-Witten theory first proposed by Siebert in 2002 and constructed in 2011 by Abramovich-Chen and Gross-Siebert. My focus will be on some of the combinatorial tools in logarithmic geometry this theory has helped illuminate, and how these tools have been useful in a broader context.