Modern power grid has a fundamental role in the operation of smart cities. However, high impact low probability extreme events bring severe challenges to the security of urban power grid. With an increasing focus on these threats, the resilience of urban power grid has become a prior topic for a modern smart city. A resilient power grid can resist, adapt to, and timely recover from disruptions. It has four characteristics, namely anticipation, absorption, adaptation, and recovery. This paper aims to systematically investigate the development of resilient power grid for smart city. Firstly, this paper makes a review on the high impact low probability extreme events categories that influence power grid, which can be divided into extreme weather and natural disaster, human-made malicious attacks, and social crisis. Then, resilience evaluation frameworks and quantification metrics are discussed. In addition, various existing resilience enhancement strategies, which are based on microgrids, active distribution networks, integrated and multi energy systems, distributed energy resources and flexible resources, cyber-physical systems, and some resilience enhancement methods, including probabilistic forecasting and analysis, artificial intelligence driven methods, and other cutting-edge technologies are summarized. Finally, this paper presents some further possible directions and developments for urban power grid resilience research, which focus on power-electronized urban distribution network, flexible distributed resource aggregation, cyber-physical-social systems, multi-energy systems, intelligent electrical transportation and artificial intelligence and Big Data technology.