Highly coordinated molecular regulation of mechanical processes is central to numerous cell processes. A key challenge in cell biophysics is, therefore, to probe intracellular force distributions and mechanical properties of live cells with high spatial and temporal resolution. This chapter describes a passive (i.e. nonperturbing) approach to map intracellular force distributions with submicron spatial resolution, and on a timescale of seconds. On the basis of a continuum mechanical interpretation of the cell cytoskeleton, this approach performs an inverse reconstruction of intracellular forces from cytoskeletal flows measured in high-resolution live cell images acquired by quantitative fluorescent speckle microscopy (qFSM). Our inverse algorithm can robustly reconstruct the relative force distribution even in the absence of a quantitative profile of network elasticity. In addition, we also propose an emerging technique for probing the in vivo actin network compliance based on correlation analysis of the same data set. We demonstrate the force reconstruction on migrating epithelial cells, where the reconstructed intracellular force field indicates spatial and temporal coordination of force generation by cytoskeleton assembly, contraction and focal adhesion resistance, and its functional output in the form of cell edge movements. This technique will potentially allow the analysis of intracellular force regulation in numerous other cell functions.