A machining installation for workpieces comprises a workpiece positioning device comprising a workpiece holder pivot unit as well as a tool positioning device comprising a tool holder pivot unit. The workpiece holder pivot unit is designed such that a workpiece holder is pivotable about at least three and no more than four workpiece holder pivot axes. Moreover, the tool holder pivot unit is designed such that a tool holder is pivotable about no more than two tool holder pivot axes. The machining installation has a simple design and ensures flexible and accurate machining of workpieces.