Following the 2003 INI programme Granular and Particle-Laden Flows, the Institute of Mathematics and its Applications has held two conferences on Dense Granular Flows at the Isaac Newton Institute: 5 - 9 January 2009 IMA Conference on Dense Granular Flows 1 - 4 July 2013 2nd IMA Conference on Dense Granular Flows Flows involving solid particulates are ubiquitous in nature and industry alike. Such flows are found in pharmaceutical production, the chemical industry, the food and agricultural industries, energy production and the environment. Many unsolved problems remain, however. For example, the rejection rate by US pharmaceutical manufacturers is around 5% with the cost of losing a single batch of medication ranging from £50,000 to £500,000. In order to be able to solve such problems, granular flows need to be understood so that their behaviour can be controlled and predicted. To date, we are able to describe rapid granular flows, where the particles are highly agitated and there has been some success describing static systems. The intermediate regime, where these two phases meet and coexist, is not as well understood and yet is the most commonly observed behaviour of granular flow. The objective of these meetings is to interface the two ends of the particulate flow spectrum – those working to understand the fundamentals of granular flows and those attempting to control particulate flows in an industrial setting - to develop solutions to the complex problems presented by dense granular flows. http://www.ima.org.uk/conferences/conferences_calendar/dense_granular_flows.cfm