This paper provides a brief history of the U.S. funding initiatives associated with promoting multiscale modeling of the physiome since 2003. An effort led in the United States is the Interagency Modeling and Analysis Group (IMAG) Multiscale Modeling (MSM) Consortium. Though IMAG and the MSM Consortium have generated much interest in developing MSM models of the physiome, challenges associated with model and data sharing in biomedical, biological, and behavioral systems still exist. Since 2013, the IEEE EMBS Technical Committee on Computational Biology and the Physiome (CBaP TC) has supported discussions on promoting model reproducibility through publications. This special issue on model sharing and reproducibility is a realization of the CBaP TC discussions. Though open questions remain on how we can further facilitate model reproducibility, accessibility, and reuse by the worldwide community for different biomedical domain applications, this special issue provides a unique demonstration of both the challenges and opportunities for publishing reproducible computational models.