Tropical geometry has nowadays several, different facets related to algebraic gometry, commutative algebra, symplectic geometry, optimization, low-dimensional topology, knot theory and physics.
In the context of enumerative geometry the idea is to replace objects from algebraic geometry by combinatorial objects, we say we tropicalize these objects. The key feature of tropicalization is that important information about the objects (related to the problem studied) is conserved.
After a recap of basic notions, I will give an overview of recent achievements of tropical enumerative geometry and discuss current directions of research.