Asynchronous Federated Learning (AFL) has been introduced to improve the efficiency of FL by reducing the latency of Machine Learning (ML) model aggregation, particularly in the Internet of Things (IoT) environment. Meanwhile, decentralized FL, such as leveraging blockchain and directed acyclic graph (DAG)-based ledgers, also has drawn much attention to the integration of FL owing to the security benefit against single-point-failure and Byzantine fault tolerant consensus. We observe that the inherent network asynchrony of DAG-based ledgers is beneficial for implementing asynchronous FL particularly in edge computing domains, even though there is no existing survey work that provides a fundamental overview of such integration. This paper surveys on the integration of asynchronous FL with DAG, which we call AFL-DAG, as a promising approach to realize the intersection of decentralized FL and asynchronous FL. Motivated by the lack of a concrete taxonomy of asynchronous FL and a global model, especially with decentralized FL, we introduce universally applicable terminologies and the extensive classification method of FL in terms of asynchrony. Based on the proposed taxonomy, we present a generic system model of AFL-DAG for edge computing applications. To provide a horizontal overview and cover fundamental concepts in AFL-DAG, we identify four critical design factors and the state-of-the-art solutions are discussed accordingly. Future directions to achieve a practical AFL-DAG are also highlighted. Finally, we explore the opportunities of AFL-DAG by investigating a popular edge computing application, the on-device crowdsourcing, and provide a high-level evaluation of AFL-DAG compared to blockchained-FL.