  Uncertainty relations take a crucial and fundamental part in the frame of
quantum theory, and are bringing on many marvelous applications in the emerging
field of quantum information sciences. Especially, as entropy is imposed into
the uncertainty principle, entropy-based uncertainty relations lead to a number
of applications including quantum key distribution, entanglement witness,
quantum steering, quantum metrology, and quantum teleportation. Herein, the
history of the development of the uncertainty relations is discussed,
especially focusing on the recent progress with regard to
quantum-memory-assisted entropic uncertainty relations and dynamical
characteristics of the measured uncertainty in some explicit physical systems.
The aims are to help deepen the understanding of entropic uncertainty relations
and prompt further explorations for versatile applications of the relations on
achieving practical quantum tasks.
