For a design to survive unforeseen physical effects like aging, temperature variation, and/or emergence of new application standards, adaptability needs to be supported. Adaptability, in its complete strength, is present in reconfigurable processors, which makes it an important IP in modern System-on-Chips (SoCs). Reconfigurable processors have risen to prominence as a dominant computing platform across embedded, general-purpose, and high-performance application domains during the last decade. Significant advances have been made in many areas such as, identifying the advantages of reconfigurable platforms, their modeling, implementation flow and finally towards early commercial acceptance. This paper reviews these progresses from various perspectives with particular emphasis on fundamental challenges and their solutions. Empowered with the analysis of past, the future research roadmap is proposed.