The efficient simulation of quantum chemistry is among the most anticipated applications of quantum computers. However, as the age of industrial quantum technology dawns, so has the realization that even “polynomial” resource overheads are often prohibitive. There remains a large gap between the capabilities of existing hardware and the resources required to quantum compute classically intractable problems in chemistry. This talk will introduce the quantum chemistry problem and several popular approaches for its solution on a quantum computer. We will then survey recent advances in the field and discuss key challenges for implementing these quantum simulations on realistic quantum computers, both in the near-term and on the first fault-tolerant devices.