This lecture will focus on the way how tropical curves appear in symplectic geometry
settings. On one hand, tropical curves can be lifted as Lagrangian submanifolds in the
ambient toric variety. On the other hand, they can be lifted as holomorphic curves.
The two lifts use two different tropical structures on the same space, related by a
certain potential function. We pay special attention to correspondence theorems
between tropical curves and real curves, i.e. holomorphic curves invariant with
respect to an antiholomorphic involution. The resulting real curves produce, in their
turn, holomorphic membranes for tropical Lagrangian submanifolds.
