When you stretch a piece of rubber, elasticity makes it spring back to its original shape. When you disturb a drop of water, on the other hand, it’s surface tension that makes it round again. Solids have surface tension too, but usually it’s so weak compared to elastic effects that it hardly matters. However, for very soft materials — things like jello, soft silicones, and even living cells — surface tension can start to dominate over elasticity, making these materials act a bit like liquids even though they are still solid. This makes for some weird physics, including solids that become stiffer when you put holes in them, and sticky solids that seem to form nearly perfectly-liquid-like bridges as you try to unstick them. To study these effects, we image the shapes made by very soft, sticky, solid silicone polymer gels while poking and pulling on them, and explore how the interplay of surface tension and elasticity produce the results we see. Our findings potentially impact any system that relies on sticky soft solids, including soft robotics, flexible and wearable electronics, microfluidics, and commercial adhesives.