Criminal courts increasingly rely upon scientific evidence provided by expert witnesses. This raises a number of questions for the courts including what type of science they should admit and who should be allowed to give such evidence. The admissibility framework for scientific evidence in England and Wales (E&W) originates from the 1975 case of R v. Turner,  QB 834. Under Turner, expert evidence is admissible as long as it is beyond the understanding of the fact-finders. This common law framework has been interpreted and developed and it now consists of a mismatch of court decisions from E&W, Australia, Canada and the United States of America (US). This framework does not seem to reflect the four decades of significant scientific advances that have taken place since Turner. There have been a number of prominent trials in the US and in E&W where scientific evidence has been associated with an improper verdict. This paper suggests that controversies related to Shaken Baby Syndrome (SBS) / Abusive Head Trauma (AHT) expose the weaknesses of admissibility frameworks in the US and, more specifically, in E&W. It concludes that the triad of symptoms frequently used to diagnose SBS/AHT is not reliable, and that courts need to consider more closely significant advances in the understanding of the symptoms previously believed to indicate that an infant had been shaken, before admitting such evidence in court.