Coordinate measuring systems are installed worldwide in factories, research and medical labs, and other industrial facilities. The purpose of the machines is to estimate how much a measured part deviates from the corresponding perfect geometry. The accuracy of the results is limited by, among other things, faulty CMS software with unknown measurement uncertainty. A record and understanding of this information is vital to industry for good results. This thesis serves as a repository and comprehensive overview of the problems with CMS software and approaches taken to solving those problems. The paper also covers new work done by the author in the areas of reference algorithm testing and verification, industry software testing via inter-comparisons with the reference algorithms, and solutions to problems similar but not identical to the fitting problems encountered in the past.