The third ML4H symposium was held in person on December 10, 2023, in New Orleans, Louisiana, USA. The symposium included research roundtable sessions to foster discussions between participants and senior researchers on timely and relevant topics for the \ac{ML4H} community. Encouraged by the successful virtual roundtables in the previous year, we organized eleven in-person roundtables and four virtual roundtables at ML4H 2022. The organization of the research roundtables at the conference involved 17 Senior Chairs and 19 Junior Chairs across 11 tables. Each roundtable session included invited senior chairs (with substantial experience in the field), junior chairs (responsible for facilitating the discussion), and attendees from diverse backgrounds with interest in the session's topic. Herein we detail the organization process and compile takeaways from these roundtable discussions, including recent advances, applications, and open challenges for each topic. We conclude with a summary and lessons learned across all roundtables. This document serves as a comprehensive review paper, summarizing the recent advancements in machine learning for healthcare as contributed by foremost researchers in the field.