In this talk I'll discuss some applications of tropical geometry to the topology of algebraic hypersurfaces due to Grigory Mikhalkin. Mikhalkin realizes a smooth complex hypersurface of any dimension as a singular torus fibration over a polyhedral complex, which is constructed by tropical methods. The smooth structure of the hypersurface is entirely enocoded in the combinatorics of this piecewise linear base. Connections with the SYZ formulation of mirror symmetry will also be discussed.