An ab initio real-space fully relativistic spin- and angle-resolved photoemission theory has been developed. The method is based on density functional theory and implemented using multiple-scattering theory with a Green's function calculated using a real-space cluster method. An efficient computer code has been developed to calculate the spectra. Interpretation of the results reveals the signatures of relativity in the photoemission spectra, and indicates what photoemission can tell us about relativistic effects in the band structure. We illustrate our theory and code by presenting results for transition metal surfaces.