This thesis presents a brief review of modern methods of phase holograms design. The simulated annealing algorithm is incorporated in the Dammann gratings to find a global solution. The theoretical basis of the binary and multi-phase holograms is given. The global strategy for the binary and multi-phase holograms design is developed. The methods to increase the computational speed of the hologram design are developed, explained and systemized. An iterative design method for electrically switchable novel liquid crystal fan-out continuous hologram using a constrained growing technique that ensures electrical conductivity is presented. In-depth analysis of methods of continuous holograms design is given with using visual design principles. Multi-phase holograms are described and digital simulation results are presented. The technique for pseudo four level sandwich holograms is described and extended. The sandwich holograms which are tolerant to 2-pixel disalignment are developed. Various types of structured overlays for sandwich holograms including overlays for error diffusion are developed and described. The comparative characteristics of the various types of phase holograms are given. This thesis presents a novel algorithm ("missing pixel holograms") for varying the intensity of a small number of output spots by taking combinations of predesigned primitive holograms with additional filling of the non-overlapped areas. The algorithm makes possible to vary the intensities of spots quickly and without further design of the holograms. The potential of phase holograms for laser beam scanning and optical interconnects are examined. Most of the simulations are approved by the optical results of highest quality. The implementations of binary holograms on SLM are made. The optical results of Dammann gratings, holographic animation, beam steering, connected holograms and others are presented. This thesis introduces a new visual approach to the holograms design and the unique software package "Holomaster 1", that allows to implement visual methods in practice. The software package incorporates many methods of holograms design developed in the thesis and summarises all our work. The wide range of the fragments of source codes in C and C++ programming languages which implement various algorithms described in the thesis are provided.