We develop a general framework for optimization and stochastic control problems on large sparse graphs, where a control is assigned to each vertex and the objective aggregates local cost functionals depending on neighboring vertices. A central question is how such problems behave as the graph grows. It turns out that locally convergent sparse graphs can have divergent optimal values. Instead, we identify local-global convergence as the appropriate notion, with graphings serving as the limiting objects. For a broad class of graph optimization problems, we prove the convergence of optimal values to their graphing counterparts and derive first-order optimality conditions for the limiting problem. Furthermore, we extend the theory to dynamic decentralized stochastic control problems and establish a stochastic maximum principle for the corresponding graphing control problem. This talk is based on a joint work with Eyal Neuman and Sturmius Tuschmann.