The evolution of folds and the origin of mineral orientations and schistosity are analytically related to the deformation paths or histories in deforming rocks. The several different finite and incremental methods of representing deformation paths are connected by matrix algebra, and graphical presentation in natural strain space is found to be particularly clear. New methods permit calculation of various components of deformation paths from boudinage, pressure shadows, and inclusion trails in naturally deformed metamorphic rocks. In coaxially accumulating deformation paths the principal strains remain parallel to the same material lines in the rock and have been referred to inappropriately as irrotational. Straight inclusion trails in metamorphic minerals may be produced by synkinematic grain growth during a coaxially accumulating path and do not necessarily indicate postkinematic grain growth. Synkinematic inclusion trails can be produced by growth of the grain through its pressure shadow rather than matrix schistosity, and the quartz protected from re-crystallization by being included in snowball garnets may sometimes form this way.