Tropical algebra is an algebra over the tropical semiring, where addition is replaced by minimum and multiplication is replaced by addition. The tropicalization process transforms polynomial equations and their solutions into discrete objects. Many properties of the original algebraic objects are present in their “tropical combinatorial shadow”. I will present some applications of tropical geometry both inside and outside mathematics. For example, I will describe some of the applications in enumerative geometry, dynamic programming, and also in phylogenetics and amplituhedron theory.