The Fram Strait is of great importance in ocean climate monitoring, as it is the only deep-water connection between the Arctic and Atlantic Oceans. Even though an extensive array of oceanographic moorings has been operated in Fram Strait since 1996 to monitor the transports through the Strait, the small spatial scales of the flow are poorly resolved, leading to large uncertainties. Beginning in the 2005-2010 DAMOCLES (Developing Arctic Modeling and Observing Capabilities for Long-term Environmental Studies) project, underwater acoustic methods were introduced to improve the monitoring of Fram Strait. A 2008-2009 pilot study with a single acoustic path was followed during 2010-2012 in the ACOBAR (ACoustic technology for OBserving the interior of the ARctic Ocean) project by the implementation of a multipurpose acoustic network with a triangle of acoustic transceivers for ocean acoustic tomography, ambient noise, and glider navigation. The measurements were continued during 2014-2016 in UNDER-ICE (Arctic Ocean Under Melting Ice), with eight acoustic paths crisscrossing the Fram Strait at 78-800N. Tomography in Fram Strait is demanding. The sound-speed field has a weak sound channel with little geometric dispersion, making it difficult to resolve and identify individual arrivals. The strong oceanographic variability in space and time reduces the coherence of the received signal and the stability of the arrival pattern. The status of tomography in Fram Strait will be summarized, focusing on the capabilities and challenges.