I will describe some instanton correction problems in mathematical physics and geometry. Recent study of these problems has produced several mysterious miracles especially when the ”instantons” are organized by highly nontrivial relations called wall crossing formulas. The study of mirror symmetry following the philosophy of Strominger-Yau-Zaslow is the main motivation but there are many other interesting connections. I will use Hitchin’s moduli spaces to illustrate main ideas. I can also explain a broader picture including fancy stuffs like black holes if time permits. The presentation will be informal and nontechnical.