Recently, intelligent reflecting surface (IRS) assisted mmWave networks are emerging, which bear the potential to address the blockage issue of the millimeter wave (mmWave) communication in a more cost-effective way. In particular, IRS is built by passive and programmable electromagnetic elements that can manipulate the mmWave propagation channel into a more favorable condition that is free of blockage via judicious joint BS-IRS transmission design. However, the coexistence of IRSs and mmWave BSs complicates the network architecture, and thus poses great challenges for efficient beam management (BM) that is one critical prerequisite for high performance mmWave networks. In this paper, we systematically evaluate the key issues and challenges of BM for IRS-assisted mmWave networks to bring insights into the future network design. Specifically, we carefully classify and discuss the extensibility and limitations of the existing BM of conventional mmWave towards the IRS-assisted new paradigm. Moreover, we propose a novel machine learning empowered BM framework for IRS-assisted networks with representative showcases, which processes environmental and mobility awareness to achieve highly efficient BM with significantly reduced system overhead. Finally, some interesting future directions are also suggested to inspire further researches.