  The uncertainty principle is a cornerstone of modern physics, and its
implications have a fundamental impact on theoretical and applied quantum
mechanics. The aim of this thesis is to study and apply the uncertainty
relations between time and energy, which are interpreted operationally as the
speed limit of quantum evolution. A geometric approach is used to derive
improved bounds for the evolution of isolated and open systems and obtain a
constructive approach for efficient and fast quantum driving. These results are
applied to set the limits for the rate of information transfer and processing,
and the power of nanomachines.
