Solar energy is globally promoted as an effective alternative power source to fossil fuels because of its easy accessibility and environmental benefit. Solar photovoltaic applications are promising alternative approaches for power supply to buildings, which dominate energy consumption in most urban areas. To compensate for the fluctuating and unpredictable features of solar photovoltaic power generation, electrical energy storage technologies are introduced to align power generation with the building demand. This paper mainly focuses on hybrid photovoltaic-electrical energy storage systems for power generation and supply of buildings and comprehensively summarizes findings of authorized reports and academic research outputs from literatures. The global installation capacity of hybrid photovoltaic-electrical energy storage systems is firstly examined to show the significant progress in emerging markets. Particularly, the latest installation status of photovoltaic-battery energy storage in the leading markets is highlighted as the most popular hybrid photovoltaic-electrical energy storage technology for building applications. The research progress on photovoltaic integrated electrical energy storage technologies is categorized by mechanical, electrochemical and electric storage types, and then analyzed according to the technical, economic and environmental performances. Moreover, extensive research on hybrid photovoltaic-electrical energy storage systems is analyzed and discussed based on the adopted optimization criteria for improving future applications in buildings. It is indicated that the lithium-ion battery, supercapacitor and flywheel storage technologies show promising prospects in storing photovoltaic energy for power supply to buildings. Potential research topics on the performance analysis and optimization evaluation of hybrid photovoltaic-electrical energy storage systems in buildings are identified in aspects of the local adaption, flexible control, grid integration, as well as building resilience and intelligence. This study provides an insight of the current development, research scope and design optimization of hybrid photovoltaic-electrical energy storage systems for power supply to buildings and can serve as an explicit guide for further research in the related area.