The ability of cells to move directionally toward areas of stiffer extracellular matrix (ECM) via a process known as 'durotaxis' is thought to be critical for development and wound healing, but durotaxis can also drive cancer metastasis. Migration is driven by integrin-mediated focal adhesions (FAs), protein assemblies that couple contractile actomyosin bundles to the plasma membrane, transmit force generated by the cytoskeleton to the ECM, and convert the mechanical properties of the microenvironment into biochemical signals. To probe the stiffness of the ECM, motile fibroblasts modulate FA mechanics on the nanoscale and exert forces that are reminiscent of repeated tugging on the ECM. Within a single cell, all FAs tug autonomously and thus act as local rigidity sensors, allowing discernment of differences in the extracellular matrix rigidity at high spatial resolution. In this article, we review current advances that may shed light on the mechanism of traction force fluctuations within FAs. We also examine plausible downstream effectors of tugging forces which may regulate cytoskeletal and FA dynamics to guide cell migration in response to ECM stiffness gradients.