A signed graph is a graph whose edges are labelled by a signature. It serves as a simple model of discrete vector bundle. We will introduce various Cheeger type constants based on vertex or edge boundaries and frustration indices, the latter of which measures how far the signature is from being balanced. Applications to the spectral theory of $p$-Laplacian on signed graphs and spectral theory of non-bipartite Cayley graphs will be discussed. This talk is based on joint works with Fatihcan Atay, Chuanyuan Ge, Chunyang Hu and Dong Zhang.