Optical components made fully or partially from reconfigurable, stimuli-responsive, soft solids or fluids-collectively referred to as soft photonics-are poised to form the platform for tunable optical devices with unprecedented functionality and performance characteristics. Currently, however, soft solid and fluid material systems still represent an underutilized class of materials in the optical engineers' toolbox. This is in part due to challenges in fabrication, integration, and structural control on the nano- and microscale associated with the application of soft components in optics. These challenges might be addressed with the help of a resourceful ally: nature. Organisms from many different phyla have evolved an impressive arsenal of light manipulation strategies that rely on the ability to generate and dynamically reconfigure hierarchically structured, complex optical material designs, often involving soft or fluid components. A comprehensive understanding of design concepts, structure formation principles, material integration, and control mechanisms employed in biological photonic systems will allow this study to challenge current paradigms in optical technology. This review provides an overview of recent developments in the fields of soft photonics and biologically inspired optics, emphasizes the ties between the two fields, and outlines future opportunities that result from advancements in soft and bioinspired photonics.