Is there a universal concept of mass in fundamental physics?

The concept of mass was introduced as a mathematical abstraction and unifying principle in physics by Newton in the 17th century, and calibrated on a Solar System scale by Cavendish at the end of the 18th century. In the 19th century, this concept proved adequate to explain a vast range of physical processes on all scales from the microscopic to the Solar System. But in the 20th century, attempts to extend this range upwards to the galactic scale, and downwards to subatomic particles, have led to increasing difficulties. Modifications to the concept of mass by Einstein and Dirac have not prevented these difficulties. In this paper, I ask the question, can these difficulties be overcome by further modification of the definitions, or is the concept of mass an unavoidably local (Solar System scale) rather than global concept?