  General properties of linear propagation of discretized light in homogeneous
and curved waveguide arrays are comprehensively investigated and compared to
those of paraxial diffraction in continuous media. In particular, general laws
describing beam spreading, beam decay and discrete far-field patterns in
homogeneous arrays are derived using the method of moments and the steepest
descend method. In curved arrays, the method of moments is extended to describe
evolution of global beam parameters. A family of beams which propagate in
curved arrays maintaining their functional shape -referred to as discrete
Bessel beams- is also introduced. Propagation of discrete Bessel beams in
waveguide arrays is simply described by the evolution of a complex $q$
parameter similar to the complex $q$ parameter used for Gaussian beams in
continuous lensguide media. A few applications of the $q$ parameter formalism
are discussed, including beam collimation and polygonal optical Bloch
oscillations. \
