The historical development of forensic inference and statistics is presented through fifteen themes that created important debates on probabilistic and statistical reasoning in forensic science. These are the need for the interpretation of scientific findings in the administration of criminal justice; the integration of scientific information with other relevant information from a particular criminal case; the separation of evidence from propositions (hypotheses) and the correct conditioning of one on the other depending on the role of the person making the judgement; quantification of the value of the evidence (with emphasis on the likelihood ratio or Bayes factor); the discrediting of the idea of a match; differing levels of hypotheses (the “hierarchy of propositions”); qualitative descriptions of the numerical value of the likelihood ratio (“verbal scales”); assumptions and statistical models for computing likelihood ratios; the debate over presenting an interval for, or a lower bound on, the likelihood ratio rather than a single value; the role of the forensic scientist in the investigation of a crime as distinct from the evaluative role at trial; probabilistic graphical networks for complicated problems of inference with many pieces of evidence; and the role of decision theory for the scientific process.