Computational protein tertiary structure prediction has made significant progress over the last decade due to the advancement of techniques and the growth of sequence and structure databases. However, it is still not very easy to predict the accuracy of a given predicted structure. Predicting the accuracy, or quality assessment of a prediction model, is crucial for a practical use of the model such as biochemical experimental design and drug design. Recently several model quality assessment programs (MQAPs) have been proposed for assessing global and local accuracy of predicted structures. We will start with reviewing the current status of protein structure prediction methods with an emphasis on the source of errors. Then existing MQAPs are classified into several categories and each is discussed. The categories include methods which evaluate the quality of template-target alignments, those which evaluate stereochemical irregularities of prediction models, and methods which integrate several features into a composite quality assessment score.