Li-ion batteries are the present and the future of energy storage. In spite of their commercial success, these devices exist in a delicate balance, and the slightest deviation from their optimal composition and operating conditions can be highly problematic. This thesis concentrates on the very events that emerge when Li-ion batteries encounter extremes: comprehensive strategies to extend the compatibility of these devices to very high temperatures are delineated; rational and experimental tools to investigate cell behavior at high power are proposed; and unconventional challenges associated with the fabrication and operation of high-energy cells are exposed. The collective work described here addresses some of the many barriers separating Li-ion batteries from a boundless future.