Monomials are single term polynomials in several variables and ideals are a convenient way of organizing them into algebraic structures. The talk will illustrate quite literally, by means of pictures, how monomials build bridges between algebra, geometry and combinatorics. We will explore this idea by focusing on what it means for a monomial ideal to exhibit symmetry with respect to a few different groups. This leads to the new notion of SSS ideals, which we study in joint work with Alessandra Costantini.