"Analytical methods are described which allow us to perform a comparative study of diffractive and non-diffractive beams and pulses. Our description first reviews basic properties of the Fresnel diffraction integral applied for calculating the propagation of well-known beams. Then different methods to obtain exact solutions to the wave equation in free space are described and their diffractive properties are analyzed. The methods described generate solutions which represent pulses or beams spatially localized and also pulses or beams that spatially propagate exhibiting spreading or diffraction, in a similar way as typical diffractive beams. Additionally, some of the solutions represent localized superluminal pulses. Computer simulations are provided to allow a comprehensive comparison of the performance of the diffractive and non-diffractive solutions."