  We present the spatially accelerating solutions of the Maxwell equations.
Such non-paraxial beams accelerate in a circular trajectory, thus generalizing
the concept of Airy beams. For both TE and TM polarizations, the beams exhibit
shape-preserving bending with sub-wavelength features, and the Poynting vector
of the main lobe displays a turn of more than 90 degrees. We show that these
accelerating beams are self-healing, analyze their properties, and compare to
the paraxial Airy beams. Finally, we present the new family of periodic
accelerating beams which can be constructed from our solutions.
