The growth and form of a soft solid pose a range of problems that combine aspects of geometry and physics. I will discuss some examples of growth and form in the plant and animal world motivated by qualitative and quantitative biological observations. The problems include the shape of a freely growing pollen tube, the undulating fringes on a leaf or petal, the folds in a mammalian brain, and the coiling of a vertebrate intestine. In each case, we will see how a combination of physical experiments, mathematical models and simple computations allow us to unravel the basis for the diversity and complexity of shape in biology.