Constructive modal logics are obtained by adding to intuitionistic logic a minimal set of axioms for the box and diamond modalities. During this talk I will present two new semantics for proofs in these logics. The first semantics captures syntactically the proof equivalence enforced by non-duplicating rules permutations, and it is defined by means of the graphical syntax of combinatorial proofs. The second semantics captures a coarse notion of proof equivalence, and it is given by means of winning innocent strategies of a two-player game over graphs encoding formulas. This latter semantics is provided with a notion of compositionality and indeed defines the first concrete model of a denotational semantics for these logics.