  The conceptual definition and understanding of the nature of time, both
qualitatively and quantitatively is of the utmost difficulty and importance,
and plays a fundamental role in physics. Physical systems seem to evolve in
paths of increasing entropy and of complexity, and thus, the arrow of time
shall be explored in the context of thermodynamic irreversibility and quantum
physics. In Newtonian physics, time flows at a constant rate, the same for all
observers; however, it necessarily flows at different rates for different
observers in special and general relativity. Special relativity provides
important quantitative elucidations of the fundamental processes related to
time dilation effects, and general relativity provides a deep analysis to
effects of time flow, such as in the presence of gravitational fields. Through
the special theory of relativity, time became intimately related with space,
giving rise to the notion of spacetime, in which both parameters cannot be
considered as separate entities. As time is incorporated into the proper
structure of the fabric of spacetime, it is interesting to note that general
relativity is contaminated with non-trivial geometries that generate closed
timelike curves, and thus apparently violates causality. The notion of
causality is fundamental in the construction of physical theories; therefore
time travel and its associated paradoxes have to be treated with great caution.
These issues are briefly analyzed in this review paper.
