In recent years there has been an increasing interest in Building-Integrated Photovoltaic (BIPV) and Building-Integrated Photovoltaic/Thermal (BIPVT) systems since they produce clean energy and replace conventional building envelope materials. By taking into account that storage is a key factor in the effective use of renewable energy, the present article is an overview about storage systems which are appropriate for BIPV and BIPVT applications. The literature review shows that there are multiple storage solutions, based on different kinds of materials (batteries, Phase Change Material (PCM) components, etc.). In terms of BIPV and BIPVT with batteries or PCMs or water tanks as storage systems, most of the installations are non-concentrating, façade- or roof-integrated, water- or air-based (in the case of BIPVT) and include silicon-based PV cells, lead-acid or lithium-ion batteries, paraffin- or salt-based PCMs. Regarding parameters that affect the environmental profile of storage systems, in the case of batteries critical factors such as material manufacturing, accidental release of electrolytes, inhalation toxicity, flammable elements, degradation and end-of-life management play a pivotal role. Regarding PCMs, there are some materials that are corrosive and present fire-safety issues as well as high toxicity in terms of human health and ecosystems. Concerning water storage tanks, based on certain studies about tanks with volumes of 300 L and 600 L, their impacts range from 5.9 to 11.7 GJprim and from 0.3 to 1.0 t CO2.eq. Finally, it should be noted that additional storage options such as Trombe walls, pebble beds and nanotechnologies are critically discussed. The contribution of the present article to the existing literature is associated with the fact that it presents a critical review about storage devices in the case of BIPV and BIPVT applications, by placing emphasis on the environmental profile of certain storage materials.