Reliability assessment tools are of crucial importance for planning and modernisation of distribution power systems. In recent years there has been an increased deployment of renewable energy, distributed generation, energy storage, electric vehicle, protection device automation and demand response schemes in the distribution networks. All these technologies contribute in their own way to network reliability. The objective of this paper is to provide a critical survey of the reliability assessment techniques used for the evaluation of distribution networks, emphasising the importance of an increased penetration of distributed energy resources and a more widespread application of control, protection and communication technologies. A detailed analysis and a comparison between different techniques and models used for the reliability assessment will be provided for each technology along with the guidelines for their application. A case study will be used to demonstrate the properties and the modelling procedure of the reliability assessment tools for modern distribution networks.