Hybrid renewable energy (HRE) system based power generation is a cost effective alternative where power grid extensions are expensive. This system utilizes two or more locally available renewable energy resources such as wind, solar, biomass, biogas and small hydro power with or without conventional fossil fuel energy sources to create standalone mode to meet the energy needs in rural remote areas. This study offers a comprehensive review of the research work carried out in planning, configurations, and modeling and optimization techniques of hybrid renewable energy systems for off grid applications. Hybrid renewable system utilities today are more dependent on an optimal design to minimize the cost function. This paper presents a review of various mathematical models proposed by different researchers. These models have been developed based on objective functions, economics and reliability studies involving design parameters. The present study will familiarize the reader with various optimization techniques of system modeling and enable them to compare these models on the basis of their cost functions. Researchers may consider the most suitable model from the various hybrid renewable system models proposed in this study to develop customized designs for optimizing system size while incurring least cost.