The dynamics of water droplets impacting on a soft dry substrate was studied experimentally. Both the drop evolution (i.e. spreading, recoiling, as well as oscillations) upon impact on a soft gel substrate (i.e. polydimethylsiloxane, PDMS) and substrate deformation caused by the impact force (for Weber numbers 110 < We < 520) were analyzed. Results were compared with similar tests carried out using hard, non-deformable PDMS substrates (two orders of magnitude more rigid than soft substrates). A sensor was designed based on the principle of a two-degree of freedom lever and successfully implemented to measure the maximum deformation of soft substrates during drop impact. Analysis of drop deformation highlighted that the recoil phase on a soft surface is slower, the final diameter of the resting drop is larger, and consequently the final resting contact angle is lower, when compared to impacts on hard substrates. Also, the oscillation time is significantly reduced, i.e. by half on soft substrates, compared to hard ones. Differences are likely due to the absorbance of impact energy due to substrate deformation. These findings are significant as for the first time it is shown that drop impact dynamics can be changed by manipulating the substrate stiffness. In addition, the following were found: drop impact can cause significant deformation of soft substrates, on the order of tens of micrometer. Different analytical models borrowed from solid mechanics of deformable bodies and drop impact on non-deformable surfaces were used and compared to estimate the force upon impact at the liquid-solid interface; in addition, a numerical model to study soft substrate deformation dynamics was developed. Analytical models significantly disagree on the magnitude of the impact force at the liquid-solid interface: model assumptions are critically discussed to explain shortcomings of such models. Numerical simulations showed that in strongly dynamic conditions, the PDMS substrate may respond to loads more rigidly than in static conditions.