Lab-on-a-chip devices leverage microfluidic technologies to enable chemical and biological processes at small scales. However, existing microfluidic channel networks are typically designed for the implementation of a single function or a well-defined protocol and do not allow the flexibility and real-time experimental decision-making essential to many scientific applications. In this Perspective, we highlight that reconfigurability and programmability of microfluidic platforms can support new functionalities that are beyond the reach of current lab-on-a-chip systems. We describe the ideal fully reconfigurable microfluidic device that can change its shape and function dynamically, which would allow researchers to tune a microscale experiment with the capacity to make real-time decisions. We review existing technologies that can dynamically control microscale flows, suggest additional physical mechanisms that could be leveraged towards the goal of reconfigurable microfluidics and highlight the importance of these efforts for the broad scientific community. [Figure not available: see fulltext.].