Second order optimization methods have the potential to be much faster than first order methods in the deterministic case, or pre-asymptotically in the stochastic case. However, traditional second order methods have proven ineffective or impractical for neural network training, due in part to the extremely high dimension of the parameter space. Kronecker-factored Approximate Curvature (K-FAC) is second-order optimization method based on a tractable approximation to the Gauss-Newton/Fisher matrix that exploits the special structure present in neural network training objectives. This approximation is neither low-rank nor diagonal, but instead involves Kronecker-products, which allows for efficient estimation, storage and inversion of the curvature matrix. In this talk I will introduce the basic K-FAC method for standard MLPs and then present some more recent work in this direction, including extensions to CNNs and RNNs, both of which requires new approximations to the Fisher. For these I will provide mathematical intuitions and empirical results which speak to their efficacy in neural network optimization. Time permitting, I will also discuss some recent results on large-batch optimization with K-FAC, and the use of adaptive adjustment methods that can eliminate the need for costly hyperparameter tuning.