Dry adhesion is governed by physical rather than chemical interactions. Those may include van der Waals and electrostatic forces, friction, and suction. Soft dry adhesives, which can be repeatedly attached to and detached from surfaces, can be useful for many exciting applications including reversible tapes, robotic footpads and grippers, and bio-integrated electronics. So far, the most studied Soft dry adhesives are gecko-inspired micro-pillar arrays, but they suffer from limited reusability and weak adhesion underwater. Recently cratered surfaces emerged as an alternative to micro-pillar arrays, as they exhibit many advantageous properties, such as tunable pressure-sensitive adhesion, high underwater adhesive strength, and good reusability. This review summarizes recent work of the authors on mechanical characterization of cratered surfaces, which combines experimental, modeling, and computational components. Using fundamental relationships describing air or liquid inside the crater, we examine the effects of material properties, crater shapes, air vs. liquid ambient environments, and surface patterns. We also identify some unresolved issues and limitations of the current approach, and provide an outlook for future research directions.