Projecting or moving up a chemical gradient is a universal behavior of living organisms. We tested the ability of S. cerevisiaea-cells to sense and respond to spatial gradients of the mating pheromone alpha-factor produced in a microfluidics chamber; the focus was on bar1Delta strains, which do not degrade the pheromone input. The yeast cells exhibited good accuracy with the mating projection typically pointing in the correct direction up the gradient ( approximately 80% under certain conditions), excellent sensitivity to shallow gradients, and broad dynamic range so that gradient-sensing was relatively robust over a 1000-fold range of average alpha-factor concentrations. Optimal directional sensing occurred at lower concentrations (5 nM) close to the K(d) of the receptor and with steeper gradient slopes. Pheromone supersensitive mutations (sst2Delta and ste2(300Delta)) that disrupt the down-regulation of heterotrimeric G-protein signaling caused defects in both sensing and response. Interestingly, yeast cells employed adaptive mechanisms to increase the robustness of the process including filamentous growth (i.e. directional distal budding) up the gradient at low pheromone concentrations, bending of the projection to be more aligned with the gradient, and forming a more accurate second projection when the first projection was in the wrong direction. Finally, the cells were able to amplify a shallow external gradient signal of alpha-factor to produce a dramatic polarization of signaling proteins at the front of the cell. Mathematical modeling revealed insights into the mechanism of this amplification and how the supersensitive mutants can disrupt accurate polarization. Together, these data help to specify and elucidate the abilities of yeast cells to sense and respond to spatial gradients of pheromone.