  We present a survey of the theory of the Lyapunov Characteristic Exponents
(LCEs) for dynamical systems, as well as of the numerical techniques developed
for the computation of the maximal, of few and of all of them. After some
historical notes on the first attempts for the numerical evaluation of LCEs, we
discuss in detail the multiplicative ergodic theorem of Oseledec \cite{O_68},
which provides the theoretical basis for the computation of the LCEs. Then, we
analyze the algorithm for the computation of the maximal LCE, whose value has
been extensively used as an indicator of chaos, and the algorithm of the
so--called `standard method', developed by Benettin et al. \cite{BGGS_80b}, for
the computation of many LCEs. We also consider different discrete and
continuous methods for computing the LCEs based on the QR or the singular value
decomposition techniques. Although, we are mainly interested in
finite--dimensional conservative systems, i. e. autonomous Hamiltonian systems
and symplectic maps, we also briefly refer to the evaluation of LCEs of
dissipative systems and time series. The relation of two chaos detection
techniques, namely the fast Lyapunov indicator (FLI) and the generalized
alignment index (GALI), to the computation of the LCEs is also discussed.
