This study was commissioned by the European Committee on Crime Problems at the Council of Europe to describe and discuss the standards used to asses the admissibility and appraisal of scientific evidence in various member countries. After documenting cases in which faulty forensic evidence seems to have played a critical role, the authors describe the legal foundations of the issues of admissibility and assessment of the probative value in the field of scientific evidence, contrasting criminal justice systems of accusatorial and inquisitorial tradition and the various risks that they pose in terms of equality of arms. Special attention is given to communication issues between lawyers and scientific experts. The authors eventually investigate possible ways of improving the system. Among these mechanisms, emphasis is put on the adoption of a common terminology for expressing the weight of evidence. It is also proposed to adopt an harmonized interpretation framework among forensic experts rooted in good practices of logical inference.