Conoscopy is the visualisation of the birefringence of materials using depolarisation of light passing through with a broad range of incident orientations. In recent years, conoscopy has become an important optical tool in the science of soft materials, such as liquid crystals and polymers, and is widely applied in materials engineering and development, for example in technologies ranging from display optics to plastic food packaging. This paper reports 'fisheye lens conoscopy', a fundamentally new and broadly applicable optical approach to conoscopy that is particularly appropriate for the study of soft materials. These capabilities are illustrated using a fisheye lens system to characterise birefringent and polarising polymer films and liquid crystal test cells. In addition to birefringence measurement, fisheye conoscopic determination of the emission characteristics of commercial light emitting devices such as liquid crystal displays and the transmission of topographically patterned light control films is presented, demonstrating that fisheye methodology can be broadly applied to determine the angular dependence of light emission or transmission in advanced optical technologies and applications.