It is common for organizations to maintain multiple variants of a given business process, such as multiple sales processes for different products or multiple bookkeeping processes for different countries. Conventional business process modeling languages do not explicitly support the representation of such families of process variants. This gap triggered significant research efforts over the past decade, leading to an array of approaches to business process variability modeling. In general, each of these approaches extends a conventional process modeling language with constructs to capture customizable process models. A customizable process model represents a family of process variants in a way that a model of each variant can be derived by adding or deleting fragments according to customization options or according to a domain model. This survey draws up a systematic inventory of approaches to customizable process modeling and provides a comparative evaluation with the aim of identifying common and differentiating modeling features, providing criteria for selecting among multiple approaches, and identifying gaps in the state of the art. The survey puts into evidence an abundance of customizable process-modeling languages, which contrasts with a relative scarcity of available tool support and empirical comparative evaluations.