The study of risk measures began in a static environment with the papers of Artzner et al. (1999) and Follmer and Schied (2002). To incorporate information structure over time, static risk measures were extended to a dynamic setting in Barrieu and El Karoui (2009), Jobert and Rogers (2008), Yong (2007) and many others. We are interested in a specific class of dynamic risk measures, namely dynamic risk measures that arise as solutions of certain types of backward stochastic differential equations (BSDEs) or backward stochastic Volterra integral equations (BSVIEs). We will discuss this connection between risk measures, capital allocations and BSDEs/BSVIEs and provide representation results for dynamic risk measures and dynamic capital allocations. These results are based on classical differentiability results for BSDEs/BSVIEs and Girsanov-type change of measure arguments. Joint work with Ludger Overbeck.