  Synchronization transitions are investigated in coupled chaotic maps.
Depending on the relative weight of linear versus nonlinear instability
mechanisms associated to the single map two different scenarios for the
transition may occur. When only two maps are considered we always find that the
critical coupling $\epsilon_l$ for chaotic synchronization can be predicted
within a linear analysis by the vanishing of the transverse Lyapunov exponent
$\lambda_T$. However, major differences between transitions driven by linear or
nonlinear mechanisms are revealed by the dynamics of the transient toward the
synchronized state. As a representative example of extended systems a one
dimensional lattice of chaotic maps with power-law coupling is considered. In
this high dimensional model finite amplitude instabilities may have a dramatic
effect on the transition. For strong nonlinearities an exponential divergence
of the synchronization times with the chain length can be observed above
$\epsilon_l$, notwithstanding the transverse dynamics is stable against
infinitesimal perturbations at any instant. Therefore, the transition takes
place at a coupling $\epsilon_{nl}$ definitely larger than $\epsilon_l$ and its
origin is intrinsically nonlinear. The linearly driven transitions are
continuous and can be described in terms of mean field results for
non-equilibrium phase transitions with long range interactions. While the
transitions dominated by nonlinear mechanisms appear to be discontinuous.
