The Wind Energy Conversion System (WECS) plays an inevitable role across the world. In particular, the attention for Permanent Magnet Synchronous Generators (PMSGs) connected with wind farm is popular. This paper deals with the literature review that describes the recent advances, progresses and innovatory trends on PMSGs for WECS. Comparison between geared and direct-driven conversion systems and the classification of electrical machines used in WECS are discussed. A detailed analysis on the design aspects considering various topologies of PMSGs are encompassed in the literature. The PMSG design and optimization problems are solved by field computation techniques and optimized by using Soft Computing (SC) techniques .The three-dimensional, finite element software platform for the analysis and design of PMSGs is discussed. This paper also deals with the interdisciplinary modeling, analysis, and optimization of PMSG using Finite Element Analysis (FEM) and SC techniques. Finally, PMSGs are reviewed and compared for further exploration.