Active materials represent a new class of condensed matter in which motile elements may collectively form dynamic, global structures out of equilibrium(1-3). Here, we present a general strategy to reconfigure active particles into various collective states by introducing imbalanced interactions. We demonstrate the concept with computer simulations of self-propelled colloidal spheres, and experimentally validate it in a two-dimensional (2D) system of metal-dielectric Janus colloids subjected to perpendicular a.c. electric fields. The mismatched, frequency-dependent dielectric responses of the two hemispheres of the colloids allow simultaneous control of particle motility and colloidal interactions. We realized swarms, chains, clusters and isotropic gases from the same precursor particle by changing the electric-field frequency. Large-scale polar waves, vortices and jammed domains are also observed, with the persistent time-dependent evolution of their collective structure evoking that of classical materials. This strategy of asymmetry-driven active self-organization should generalize rationally to other active 2D and three-dimensional (3D) materials.