Two-mirror telescopes possess an agreeable tradeoff between performance and complexity that suits the needs of many scientific tasks, and recent developments in manufacturing technology have enabled unobscured two-mirror designs with freeform surfaces. We illustrate how structural aberration coefficients reveal the fundamental aberration characteristics of such systems and provide a summary table of general solutions that prescribe freeform surface shapes and tilts. Two unobscured design forms with remarkable aberration cancellation, inspired by well-known on-axis anastigmatic solutions, are presented.