Emergency response to incidents such as accidents, crimes, and fires is a major problem faced by communities. Emergency response management comprises of several stages and sub-problems like forecasting, resource allocation, and dispatch. The design of principled approaches to tackle each problem is necessary to create efficient emergency response management (ERM) pipelines. Over the last six years, we have worked with several first responder organizations to design ERM pipelines. In this paper, we highlight some of the challenges that we have identified and lessons that we have learned through our experience in this domain. Such challenges are particularly relevant for practitioners and researchers, and are important considerations even in the design of response strategies to mitigate disasters like floods and earthquakes.