Wind energy is an effective and promising renewable energy source to produce electrical energy. Wind energy conversion systems (WECS) have been developing on a wide scale worldwide. The expansion of wind energy demand tends to produce high-quality output power in terms of grid integration. Due to the intermittent nature of wind energy, great challenges are found regarding WECS modeling, control, and grid integration. This paper introduces a comprehensive review of WECS and their grid-interface systems based on soft computing methods. To achieve this aim, more than 300 articles are organised and only 160 papers are presented in this review. This is intended to cover a broad range of topics concerning the configurations of WECS, electrical generators, and various topologies of power converters used for control and grid integration. Furthermore, international grid codes for wind energy integration with electric grids, particularly frequency, power factor, and low voltage ride through (LVRT) capability are investigated. The major controller approaches and topologies for grid and generator converters are discussed. Different aspects of modern control of WECS are introduced either for grid-side or generator-side. Moreover, control strategies for maximum power point tracking methods are compared along with methods of frequency control. This review paper introduces a comprehensive and a useful summery for the recent work in literature regarding WECS. Detailed modelling, control, and grid integration along with comparisons and discussion are introduced.