LES is expected to become a powerful tool for turbulent flow calculations of practical interest in the near future. The paper is concerned with the development and first applications of a LES technique based on an explicit finite-volume method for curvilinear body-fitted grids suitable to simulate flows in or around complex geometries. Two different subgrid-scale models are implemented and tested. For the near-wall treatment different wall function approaches as well as no-slip boundary conditions can be applied. This technique has been used to simulate six different internal and external flow configurations: plane channel flow, flow through a straight square duct and a 180 degree bend, flow around a surface-mounted cubical obstacle and the flow past a long, square as well as a circular cylinder. For four test cases results are discussed in detail and compared with experimental data available. The influence of different aspects of a LES method (e.g. resolution, subgrid-scale modelling, wall boundary conditions) are investigated.