Abstract: Collective decision-making plays a central part in the lives of many social animals. Two important factors that influence collective decision-making are information uncertainty and conflicting preferences. Here, I bring together, and briefly review, basic models relating to animal collective decision-making in situations with information uncertainty and in situations with conflicting preferences between group members. The intention is to give an overview about the different types of modelling approaches that have been employed and the questions that they address and raise. Despite the use of a wide range of different modelling techniques, results show a coherent picture, as follows. Relatively simple cognitive mechanisms can lead to effective information pooling. Groups often face a trade-off between decision accuracy and speed, but appropriate fine-tuning of behavioural parameters could achieve high accuracy while maintaining reasonable speed. The right balance of interdependence and independence between animals is crucial for maintaining group cohesion and achieving high decision accuracy. In conflict situations, a high degree of decision-sharing between individuals is predicted, as well as transient leadership and leadership according to needs and physiological status. Animals often face crucial trade-offs between maintaining group cohesion and influencing the decision outcome in their own favour. Despite the great progress that has been made, there remains one big gap in our knowledge: how do animals make collective decisions in situations when information uncertainty and conflict of interest operate simultaneously?