Several factors acting together have recently enabled clinicians to seriously consider whether chronic immunosuppression is needed in all solid organ allograft recipients. This has prompted a dozen or so centers throughout the world to prospectively wean immunosuppression from conventionally treated liver allograft recipients. The goal is to lessen the impact of chronic immunosuppression and empirically identify occasional recipients who show operational tolerance, defined as gross phenotype of tolerance in the presence of an immune response and/or immune deficit that has little or no significant clinical impact. Rare operationally tolerant kidney allograft recipients have also been identified, usually by single case reports, but only a couple of prospective weaning trials in conventionally treated kidney allograft recipients have been attempted and reported. Pre- and postweaning allograft biopsy monitoring of recipients adds a critical dimension to these trials, not only for patient safety but also for determining whether events in the allografts can contribute to a mechanistic understanding of allograft acceptance. The following is based on a literature review and personal experience regarding the practical and scientific aspects of biopsy monitoring of potential or actual operationally tolerant human liver and kidney allograft recipients where the goal, intended or attained, was complete withdrawal of immunosuppression.