This work addresses the retrieval of the three water quality parameters chlorophyll-a, yellow substance and suspended particulate matter from spectra of remote sensing reflectance in European coastal waters. We study the suitability of a semi-analytical algorithm for the retrieval of these parameters in coastal waters to investigate the validity of radiative transfer theory and bio-optical models that have been developed primarily for open ocean waters. To obtain water quality parameters from reflectance measurements we employ a non-linear inversion method (Gauss-Newton). Algorithm parameters are established to ensure convergence of the method and reduce trapping by local minima. The developed algorithm is then evaluated with the help of a case-specific sensitivity analysis that reveals strengths and weaknesses with respect to measurement errors and inaccuracies of the bio-optical models on which the algorithm is based. In order to establish the validity of the results, a second sensitivity analysis is carried out based on the analysis of normalised partial derivatives of the algorithm's central equation. The algorithm is then applied to an extensive in situ data set consisting of 447 high-resolution spectra of remote sensing reflectance and water quality parameters from a range of European coastal waters, acquired in the framework of three different projects. Given the different measurement techniques within the various projects, it is not surprising that the algorithm performs poorly for the complete data set. Studying the regional subsets individually yields improved results in some cases, suggesting potential for developing regionally specific algorithms on the basis of dedicated tuning. The complete failure of the algorithm in other regions displays the shortcomings of the methodology. It is shown that, in some cases, the forward model fails to describe the optical characteristics encountered producing a pronounced mismatch between calculated and measured reflectance spectra in both spectral shape and magnitude. In other regions the spectral shape is largely reproduced by the model but a mismatch in magnitude results in failure of the inversion procedure. However, the most fundamental problem encountered is the non-uniqueness of the reflectance inversion process for some spectra. Improved bio-optical models and dedicated measurement campaigns in coastal waters are a crucial requirement to resolve this problem for future regional applications of semi-analytical algorithms. We point out the optical characteristics of favourable and unfavourable conditions for the retrieval of water quality parameters and provide some guidelines to future measurements of optical properties of coastal waters.