We present several experiments that allow us to show the intensity and phase structure of transverse modal patterns, Hermite-Gaussian and Laguerre-Gaussian laser modes and dynamical transverse patterns. These new spatial configurations of the light depend on the dynamics of laser resonator, and on the boundary conditions. The Laguerre-Gaussian modes are obtained either by the direct conversion of Hermite-Gaussian modes using a modal converter or with a computer-generated hologram. The modal converter is based on a cavity of cylindrical lenses. We analyse the phase structure and optical phase singularities of laser modes with a Mach-Zehnder interferometer. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre-Gaussian modes, which is the origin of the orbital angular momentum associated with each one of them. Moreover, we try to give an explanation of the new modal patterns observed.