High step-up boost converters with coupled inductor have attracted much attention in the fuel cell or photovoltaic grid-connected generation system, however, there are few literatures elaborated on the construction ideas and derivation methods of them. Accordingly, in order to obtain a clear roadmap on the derivation and inner connection of these converters, a comprehensive review and analysis are presented in this paper. First, the basic boost converter with coupled inductor is regarded as the basic topology, and its merits and demerits are analyzed in detail. Then, in order to address these demerits, various step-up techniques are introduced, such as the rectifier circuit, the active-clamped circuit, the multi-winding coupled inductor, and the voltage doubler rectifier; and numerous new topologies are continuously proposed by combinations and equivalent simplifications. In addition to a detailed synthesis of each topology, a comparative and quantitative analysis among some important converters is presented, and the optimal one is chosen to build a 250 W prototype. Finally, based on comparisons and analysis, the main characteristics and inner connections of these high step-up boost converters with coupled inductor are identified and clarified.