Unlike rigid substrates, a sessile drop can deform a soft substrate by capillary forces, with the deformation being inversely proportional to the substrate modulus. The substrate deformation can affect the contact angle and contact angle hysteresis, and thus various capillary phenomena. The first part of this presentation will focus on the effects of substrate stiffness on spontaneous wetting. We show that the early stage of fast wetting of soft substrates is dominated by inertia, which is similar to that on rigid substrates, and the wetting dynamics follows a power law depending on wettability, but not on stiffness. However, the duration of the fast inertial wetting is controlled by substrate stiffness. This is an indication of a viscoelastic dissipation process occurring during wetting that starts after some characteristic time dependent on the surface tension of the liquid, on the viscosity of the surface, and on the speed of wetting. In the second part of the talk, drop impact dynamics on different soft substrates will be introduced. Several impact phenomena, which depend on the dynamic interaction between impinging droplets and soft substrates, were identified. We demonstrate that the effect of surface stiffness on drop impact is related to the dynamic response of viscoelastic substrates to impact. We also show that the dynamic wettability of soft substrates affects the post-impact droplet oscillations.