Work in the field of AI over the past twenty years has shown that many problems can be represented as constraint satisfaction problems and efficiently solved by constraint satisfaction algorithms. However, constraint satisfaction in its pure form isn't always suitable for real world problems, as they often tend to be inconsistent, which means the corresponding constraint satisfaction problems don't have solutions. A way to handle inconsistent constraint satisfaction problems is to make them fuzzy. The idea is to associate fuzzy values with the elements of the constraints, and to combine these fuzzy values in a reasonable way, i.e., a way that directly corresponds to the way how crisp constraint problems are handled.The purpose of this paper is to briefly introduce a framework for fuzzy constraint satisfaction problems and to discuss some heuristics for solving them efficiently.