In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space X coarsely (resp. uniformly) embeds into a Banach space Y by a weakly sequentially continuous map, then every spreading model (en)n of a normalized weakly null sequence in X satisfieswhere δ Y is the modulus of asymptotic uniform convexity of Y . Among many other results, we obtain Banach spaces X and Y so that X coarsely (resp. uniformly) embeds into Y , but so that X cannot be mapped into Y by a weakly sequentially continuous coarse (resp. uniform) embedding.