The purpose of this article is to present the results obtained in a study of summative assessment in practical translation modules in translation degree programs in Spain and of the problems that exist in relation to assessment. Part of the EACT project, the study was conducted as a survey, using a specifically designed questionnaire. Its sample comprised 97 translator trainers who, between them, taught a total of 223 practical written translation modules. This article presents the profile of those trainers, the modules they habitually taught and the assessment tasks they used for grading in each module. Among the most common of those tasks are translations of texts, translation projects, students’ commentaries or reports on their own translations, translation error analysis and the analysis of the linguistic, textual and pragmatic characteristics of source texts. The article also identifies some of the main problems and challenges related to assessment in translation teaching, which notably include the subjectivity inherent in any type of assessment, the lack of standardisation of assessment procedures and the heterogeneity of translation students. It concludes by outlining the contribution of the EACT project, a key aspect of which is the design of translation-level tests.