We overview recent results on dynamical systems approach to analysis and design of electricity grids. The first topic is the phenomenology of one type of short-term swing instabilities in multi-machine grids, which is termed the Coherent Swing Instability. The second topic is the design of electricity grid for management of multiple households. These apparently different topics are discussed from the common perspective of dynamical systems theory, that is, high-dimensional oscillatory systems with dominant inertia.