Tropical ideals are the building blocks for the theory of tropical schemes, which are part of a program to build foundations for tropical geometry. From a matroid perspective, they are "towers" of (valuated) matroids: for each degree d we give a (valuated) matroid on the set of monomials of degree d in a polynomial ring. I will introduce this theory, and explain the relevance of better understanding these matroids for tropical and algebraic geometry.