Explore quantum algorithms for Hamiltonian simulation in this comprehensive lecture by Nathan Wiebe from the University of Washington. Delve into the recent advancements in quantum algorithms that have revolutionized simulations in chemistry, condensed matter systems, and various other applications. Gain a high-level understanding of key strategies employed in modern Hamiltonian simulation algorithms, learning how they work and how to apply them to different problem features. Discover how these methods can be optimized for simulations in chemistry and quantum electrodynamics. Examine topics such as Trotter-Suzuki simulations, interaction picture simulation, reflection operations, and qubitization in chemistry. Conclude by exploring open problems and new opportunities created by these emerging paradigms in quantum simulation and beyond.