In this contribution, the Bayesian framework for interpretation of evidence when applied to forensic speaker recognition is introduced. Different aspects of the use of voice as evidence in the court are addressed, as well as the use by the forensic expert of the likelihood ratio as the right way to express the strength of the evidence. Details on computation procedures of likelihood ratios (LR) are given, along with the assessment tools and methods to validate the performance of these Bayesian forensic systems. However, due to the practical scarcity of suspect data and the mismatched conditions between traces and reference populations common in daily casework, significant errors appear in LR estimation if specific robust techniques are not applied. Original contributions for the robust estimation of likelihood ratios are fully described, including TDLRA (target dependent likelihood ratio alignment), oriented to guarantee the presumption of innocence of suspected but non-perpetrators speakers. These algorithms are assessed with extensive Switchboard experiments but moreover through blind LR-based submissions to both NFI-TNO 2003 Forensic SRE and NIST 2004 SRE, where the strength of the evidence was successfully provided for every questioned speech-suspect recording pair in the respective evaluations.