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Interest in coherent remote sensing systems has stimulated investigations in the properties laser propagation through extended atmospheric turbulence. This thesis investigates the statistics of phase, and phase related, observables using analytical and computational techniques, together with experimental results. The phase screen technique is used to simulate perturbations to the refractive index of a medium through which the radiation propagates. Several different turbulence models (Gaussian correlated noise, Kolmogorov turbulence, Tatarski and Von Karman spectral models) are investigated, and their relative merits for describing experimental conditions and descriptive statistical measures are compared and contrasted. The phase power spectrum is crucial to an understanding of the practical operation of a coherent imaging system, and later part of the thesis is devoted to the investigation of a LIDAR system in particular. Several turbulence regimes are investigated, from an analytical treatment of a weakly turbulent, extended atmosphere, to large 3D computations designed to simulate experimental arrangements. The 3D simulation technique presented herein has been developed to allow for the investigation of temporal statistics. New power law behaviours are found to appear in temporal frequency spectra which differ from the -8/3 power law form that has been accepted in much of the literature. Strongly turbulent regimes result in a -2 power law while the use of a Gaussian beam profile in an extended medium gives a -11/3 power law under weak turbulence conditions. Please note: Pagination in electronic reproduction differs from print original. The print version is the version of record.