The tropical (or min-plus) semiring appears in a plethora of areas, among them, algebraic geometry, optimization, and 'dequantization' in quantum physics. Motivated by time series analysis, we introduce the concept of quasisymmetric functions over the tropical (or, in fact, any commutative) semiring and investigate their algebraic setting. Joint work with Kurusch Ebrahimi-Fard (NTNU Trondheim) and Nikolas Tapia (WIAS Berlin).