The time-varying reproduction number (R_t) is an important measure of transmissibility during outbreaks. Estimating whether and how rapidly an outbreak is growing (R_t > 1) or declining (R_t < 1) can inform the design, monitoring and adjustment of control measures in real-time. We use a popular R package for R_t estimation, EpiEstim, as a case study to evaluate the contexts in which R_t estimation methods have been used and identify unmet needs which would enable broader applicability of these methods in real-time. A scoping review, complemented by a small EpiEstim user survey, highlight issues with the current approaches, including the quality of input incidence data, the inability to account for geographical factors, and other methodological issues. We summarise the methods and software developed to tackle the problems identified, but conclude that significant gaps remain which should be addressed to enable easier, more robust and applicable estimation of R_t during epidemics.