In this survey, we review the literature investigating participatory budgeting as a social choice problem. Participatory Budgeting (PB) is a democratic tool aiming at making budgeting decisions in a more democratic manner. Specifically, citizens are asked to vote on who to allocate a given amount of money to a set of projects that can potentially be funded. From a social choice perspective, it corresponds then to the problem of aggregating opinions about which projects should be funded, into a budget allocation satisfying a budget constraint. is problem has received substantial a ention in recent years and the literature is growing at a fast pace. In this survey, we present the most important research directions from the literature, each time presenting a large set of representative results. We only focus on the indivisible case, that is, PB problems in which projects can either be fully funded or not at all. e aim of the survey is to present a comprehensive overview of the state of the research on PB. We aim at providing both a general overview of the main research questions that are being investigated, and formal and unified definitions of the most important technical concepts from the literature.Of course a survey is never complete as the state of the research keeps changing. is document is intended to be a living document that gets updated every now and then as the literature grows. If you feel that some papers are not presented correctly, or simply missing, feel free to contact us. We will be more than happy to correct it.⋆ Laruelle (2021) considers that the agents submit weak and complete rankings over the projects, that are then converted into cardinal scores (via positional scoring functions) for the aggregation.