The increasing effects of climate change and extreme weather events on the operation of power systems highlight the need for developing effective techniques and models for evaluating the challenges that power systems may have to deal with in the future for maintaining high levels of resilience. Within this context, the aim of the `Resilient Electricity Networks for Great Britain (RESNET)' project is to develop and demonstrate a comprehensive approach to analyse the effects of climate-related changes on the resilience of the Great Britain's electricity system, and to develop tools for quantifying the value of adaptation measures that would enhance its resilience. This paper presents an overview of the key research activities and findings of RESNET project, specifically addressing possible climate change implications related to demand and supply scenarios, component ratings, and impact of extreme weather on system reliability. The final aim is to provide insights on various climate and weather-related challenges that the Great Britain's electricity system might face in the future.