Connective tissues provide mechanical support and frameworks for the other tissues of the body. Type 1 collagen is the major protein component of ordinary connective tissue, and fibroblasts are the cell type primarily responsible for its biosynthesis and remodeling. Research on fibroblasts interacting with collagen matrices explores all four quadrants of cell mechanics: pro-migratory vs. pro-contractile growth factor environments on one axis; high tension vs. low tension cell-matrix interactions on the other. The dendritic fibroblast - probably equivalent to the resting tissue fibroblast - can be observed only in the low tension quadrant and generally has not been appreciated from research on cells incubated with planar culture surfaces. Fibroblasts in the low tension quadrant require microtubules for formation of dendritic extensions, whereas fibroblasts in the high tension quadrant require microtubules for polarization but not for spreading. Ruffling of dendritic extensions rather than their overall protrusion or retraction provides the mechanism for remodeling of floating collagen matrices, and floating matrix remodeling likely reflects a model of tissue mechanical homeostasis.