Cost assessments of damages of, prevention of, and responses to natural hazards provide crucial information for decision support and policy development in the fields of natural hazard management and planning for adaptation to climate change. There is a considerable diversity of methodological approaches and terminology being used in costs assessments of different natural hazards. This complicates the assessment of comprehensive, robust and reliable costs figures, as well as comparison of costs across hazards and impacted sectors. This report is part of the EU project ConHaz. The first objective of ConHaz is to compile state-of-the-art methods and terminology as used in European case studies. This compilation will consider droughts, floods, storms, and alpine hazards, as well as various impacted sectors, such as agriculture, health and nature. It will consider direct, indirect and intangible costs. ConHaz further examines the costs and benefits of risk-prevention and emergency response policies. The second objective of ConHaz is to evaluate the compiled methods by considering theoretical assumptions underlying cost assessment methods and issues appearing in application of the methods, such as availability and quality of data. ConHaz will also assess the reliability of the end results by considering the accuracy of cost predictions and best-practice methods of validation, and will identify relevant gaps in assessment methods. The third objective of ConHaz is to compare available assessment methods with end-user needs and practices, so as to better identify best practice and knowledge gaps in relation to policy-making. A final objective of ConHaz is to give recommendations about best practices and to identify resulting research needs.