By introducing the notion of compositionals we obtain a combinatorial interpretation of plethysm of formal power series in infinitely many variables. The following related problems are studied: Pólya's theorem on the plethysm of cycle indices, plethystic inverse, the inverse of a sequence of delta series, the plethystic analog of the partition lattice, the reduced incidence algebra of the plethystic lattice, and the plethystic Hopf algebra. We also introduce plethystic trees, enriched plethystic trees and plethystic Schröder trees. An involution for plethystic Schröder trees is devised, which leads to a combinatorial expansion for the plethystic inverse of a series f(x₁,x₂,…) containing the factor x₁.