Machine learning is fast emerging as a potential disruptive tool to tackle longstanding research problems across the sciences. This is mainly driven by its ability to find complex patterns in large datasets, often without the need for feature extraction or engineering. It comes as no surprise that geophysicists, like domain experts from other scientific disciplines, are starting to find value in machine learning methods. In particular, recent advances in the field of Scientific Machine Learning demonstrate its largely untapped potential for longstanding challenges in the field of computational geophysics. In this talk, I will summarize our efforts on the use of physics-informed neural networks (PINNs) for solving seismic modeling and inverse problems. In addition to addressing the computational bottleneck associated with conventional algorithms, I will demonstrate how PINNs allow the freedom to incorporate complete physics of wave propagation instead of relying on approximations. I will also discuss the applicability of PINNs to develop real-time microseismic monitoring solutions for assessing and mitigating induced seismicity hazard due to anthropogenic activities such as underground mining, hydraulic fracturing and CO₂ geological sequestration.