Photovoltaic (PV) power systems have been in the spotlight of scientific research for years. However, this technology is still undergoing developments, and several new architectures are proposed each year. This study describes the main challenges facing grid-connected PV systems without galvanic isolation, then carries out a review of the state-of-the-art of single-phase systems. The converter topology review is focused on the match between the different types of converters and the different PV panel technologies, determined by the common-mode voltage between the PV string terminals and the ground. The ground leakage current, due to time variations of this voltage, is a source of electric safety and electromagnetic interference (EMI)-related problems, and its amplitude is constrained by international standards. The basic principles of operation of the different solutions are described, along with their strengths and drawbacks. Conversion efficiency is evaluated qualitatively comparing the semiconductor power losses. Finally, the future trends regarding semiconductor devices, PV panels and international regulations for single-phase grid-connected equipment are discussed, and indications on how these might steer future research efforts in PV converters are inferred