It is very attractive to apply a directly modulated laser (DML)-based intensity-modulation and direct-detection (IM/DD) system in future data centers and 5G fronthaul networks due to the advantages of low cost, low system complexity, and high energy efficiency, which perfectly match the application scenarios of the data centers and 5G fronthaul networks, in which a large number of high-speed optical interconnections are needed. However, as the data traffic in the data centers and 5G fronthaul networks continues to grow exponentially, the future requirements for data rates beyond 100 Gbaud are challenging the existing DML-based IM/DD system, and the main bottleneck is the modulation bandwidth of the DML. In this paper, the data rate demands and technical standards of the data centers and 5G fronthaul networks are reviewed in detail. With the modulation bandwidth requirements, the technical routes and achievements of recent DMLs are reviewed and discussed. In this way, the prospects, challenges, and future development of DMLs in the applications of future data centers and 5G fronthaul networks are comprehensively explored.