We model customer mobility and congestion in supermarkets and investigate how these two processes depend on the layout of a store. Our motivation is twofold: we seek to understand how customers move in supermarkets and how to arrange the layout of a supermarket to reduce congestion in it. Congestion affects both the shopping experience and the bottom line of supermarkets, so models that can estimate customer mobility and congestion in new store layouts are of great interest to retailers. We use random-walk models and population-level mobility models to model customer mobility, and we use queues and queueing networks to model congestion. We represent a store as a network in which the nodes are zones in a supermarket and edges connect adjacent zones. Customers traverse the network from node to node and queue at each node. We measure congestion by the total mean queue size Q (which is equivalent to the total number of customers in a store). We are interested in how network topology (representing store layout) affects Q. We first examine a simple model of single-source, single-sink queueing networks with unbiased random walkers. We analyse the relationship between congestion (specifically, Q) and network topology, and we describe network topologies that minimize Q. We also present efficient greedy algorithms for edge addition and deletion to reduce Q. We then consider human-mobility models and use them to estimate mobility flows between zones in a supermarket. These models have, to our knowledge, not been applied previously to problems with such small spatial scales. We applied the human-mobility models to 17 supermarkets, and we find that they can successfully estimate 65-70% of the mobility flow in a supermarket. We also find that the parameters in our models do not change markedly between different stores and different time periods of the same store. One can therefore calibrate the parameters of our models on one store and then use the models to estimate mobility flow in all other stores using only purchase data and the store layouts. Finally, we integrate the human-mobility models into a queueing-network framework to estimate congestion in supermarkets. We present a simple optimization algorithm that swaps the locations of aisles and finds store layouts with significantly smaller values of Q. In these store layouts, popular nodes are often moved from the centre of a store to the perimeter. Our research helps improve understanding of customer mobility and congestion in supermarkets, especially the relationship between congestion and store layout. Our models and ideas are also relevant for complex systems on similar spatial scales (eg, mobility of visitors in a museum).