Magnetic flux ropes manifest as twisted bundles of magnetic field lines. They carry significant amounts of solar mass in the heliosphere. This paper underlines the need to advance our understanding of the fundamental physics of heliospheric flux ropes and provides the motivation to significantly improve the status quo of flux rope research through novel and requisite approaches. It briefly discusses the current understanding of flux rope formation and evolution, and summarizes the strategies that have been undertaken to understand the dynamics of heliospheric structures. The challenges and recommendations put forward to address them are expected to broaden the in-depth knowledge of our nearest star, its dynamics, and its role in its region of influence, the heliosphere.