Since the emergence of Bitcoin in 2008, various decentralized consensus schemes have been brought about to realize a decentralized ledger. Most existing schemes adopt a blockchain, which is the fundamental building block of the consensus of Bitcoin, to store and extend the ledger. However, classical blockchain is heavily bounded in its scalability. Specifically, its throughput of transactions is far from satisfactory and transactions are confirmed at a slow rate, which greatly limit the practical application of blockchain. To face this issue, novel consensus schemes based on direct acyclic graphs (DAGs) are introduced in an attempt of achieving better performance. Due to its high concurrency feature, the research of DAG-based distributed ledger is getting more and more attention. With a systematic survey, it is proposed that DAG ledgers can be classified into three categories by the feature of its underground consensus mechanisms, i.e., DAG with a main chain, DAG of parallel chains, and naive DAG. To begin with, the pivotal features and characteristics of current consensus system associated with each category are introduced. After that, a comprehensive evaluation regarding different aspects of current systems is conducted. Finally, several open challenges on DAG-Based consensus schemes are identified to consider in future research endeavors.