In this talk we consider holomorphic embeddings of Gr(2,m) into Gr(2,n). We can study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. Using the relations between Chern classes of the universal bundles and Schubert cycles, together with properties of holomorphic vector bundles of rank 2 on Grassmannians, we find conditions on m and n for which any holomorphic embedding of Gr(2,m) into Gr(2,n) is linear.