To facilitate the energy transition towards a decarbonized energy sector, distribution system operators will have to address several challenges by upgrading and redesigning the operation of the distribution grid. This review paper presents an overview of the operational challenges of low voltage distribution grids (LVDGs) operating under a high penetration of photovoltaic systems (PVs) and electric vehicles (EVs). Specifically, the impacts of PVs and EVs on the voltage profile, net-demand profile and network congestion, as well as network asymmetry are demonstrated and discussed. This is achieved by utilizing real measurements from LVDGs in the Cyprus power system and by examining different case studies that consider future operating conditions. A detailed review of management solutions available in the literature for active LVDGs is then presented that aim to mitigate the detrimental impacts of PVs and EVs. These include wired solutions such as on-line-tap changing transformers, reactive power control by smart inverters, active power control through PV curtailments, energy storage systems, EV charging strategies, and phase balancing schemes. In addition, several management solutions are implemented to representative LV feeders, which have been made publicly available, where their effectiveness and potential areas of improvement are evaluated.