A market review on Hybrid Inverters with Back-Up (HIBU) is presented, selecting products from eleven global inverter manufacturers. A systemic review of all the productsis performed, along with a general comparison of their main features. Trends in power ranges, battery voltages, back-up connection scheme and switching times are then highlighted and other more peculiar characteristics are assessed. A focus on potential applications in the Swedish market is put, considering an average Swedish household consumption profile. Ten from the available software for modeling photovoltaics applications are then reviewed finding PVsyst, Homer and SAM the most suitable tools for computing systems with HIBU. Finally, a case study is simulated on PVsyst showing the influence of the battery size on the percentage of covered load for different values of grid availability. The influence of different locations and different battery discharging strategies is also assessed, critically evaluating the reliability of the model used on PVsyst and stating the main shortcomings.