We investigate the dynamics of drop impacts on dry solid surfaces. By synchronizing high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers (Re). At high Re, we show that the early-time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. When viscous forces gradually set in with decreasing Re, we analyze the early-time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the maximum impact force and the associated peak time. Lastly, we also investigate the spreading of liquid drops at high Re following the initial impact. We find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops. Our study provides a quantitative understanding of the temporal evolution of impact forces and sheds new light on the self-similar dynamics of drop-impact processes.