The intensity of the solar radiations falling on the earth surface ranges between 5 and 7.5 kWh/m2/day. For the non-directed solar thermal application, higher intensity level is required. The Concentrating Solar Power (CSP) technology incorporating reflecting mirrors reinforces the solar radiations with high intensity. It is suitable for various applications; that is, space heating, space cooling, and cooking, steam, and power generation without any polluted emissions. Meanwhile, among the various CSP technologies, the Concentrating Solar Parabolic Dish Stirling engine System (CSP-DSS) has got attention of the research community due to its various attractive features. The output power and efficiency of the CSP-DSS depend upon their geometrical, optical, and operating parameters. It is therefore, necessary to mathematically investigate the influence of these parameters on system performance before its design and installation. In the existing literature reported, only some specific parameters of the CSP-DSS have been focused and considered to investigate the system performance. To the best of author's knowledge, no literature has been found to provide the mathematical modeling of all the system parameters in a single manuscript to study and investigate their influence on the system performance. Hence, this review article aims to compile, expansively review and organize the systematical mathematical modeling for all optical, geometrical, and operating parameters of the CSP-DSS along with the system design methodology. Likewise, the effects of these parameters on the system output power and efficiency under various operating conditions have been investigated. In addition, comprehensive study of CSP-DSS components along with their classification have been painstakingly discussed to determine optimal system configuration. Finally, the latest review study in the field of CSP-DSS have been deeply and comprehensively discussed. This review study concludes that, the kinematic gamma type Stirling engine coupled with Permanent Magnet DC generator (PMDC) and Azimuth-Altitude Dual Axis Tracker (AADAT) could be the better CSP-DSS design and configuration in context of the standalone off-grid electricity generation system.