  Some aspects of the predictability problem in dynamical systems are reviewed.
The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon
entropy and algorithmic complexity is discussed. In particular, we emphasize
how a characterization of the unpredictability of a system gives a measure of
its complexity. A special attention is devoted to finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system.
