This paper is a submission for the special call for survey papers. We comprehensively review the field of neurosymbolic answer set programming (ASP). The scope is clearly defined: we include all papers from the last five years that combine a neural component and a sufficiently expressive ASP component (at least at the level of stratified programs) in a supervised learning setting. The survey includes both an overview of frameworks in this field, as well as a thorough discussion of limitations and open challenges. We have made efforts to ensure that this survey accessible for researchers new to this topic. All terms used in the main paper are defined in the background section. We also include twelve illustrations that visualise the different frameworks. They were made from the ground up for this survey and use consistent shapes and terminology, which allows the reader to compare and contrast the different approaches. As an expressive logical language, ASP is popular among neurosymbolic researchers and has an active and engaged community. We believe that this survey paper will benefit the community by providing a clear overview of neurosymbolic ASP and its open challenges, enabling interested researchers to get familiar with the field and contribute to it in the future.