I will outline the construction of isomonodromic families of irregular meromorphic connections on ${\mathbf P}^1$ with values in the derivations of a class of infinite-dimensional Poisson algebras, and describe two of their scaling limits. In the "conformal limit" we recover a version of the connections introduced by Bridgeland and Toledano Laredo, while in the "large complex structure limit" the connections relate to tropical curves in the plane and, through work of Gross, Pandharipande and Siebert, to tropical/GW invariants. This is joint work with M. Garcia-Fernandez and J. Stoppa.