Flood risk assessment is an essential part of flood risk management, a concept that is becoming more and more popular in European flood policy and is part of the new European Union flood directive. This paper gives a brief introduction into the general concept and methods of flood risk assessment. Furthermore, 3 problems in the practical application of flood risk assessment, particularly on the river basin scale, are discussed: First, uncertainties in flood risk assessment; second, the inclusion of social and environmental flood risk factors; and third, the consideration of the spatial dimension of flood risk. In the 2nd part of the paper a multicriteria risk mapping approach is introduced that is intended to address these 3 problems.