  We use analytical methods to investigate cellular automata for traffic flow.
Two different mean-field approaches are presented, which we call site-oriented
and car-oriented, respectively. The car-oriented mean-field theory yields the
exact fundamental diagram for the model with maximum velocity $\vm =1$ whereas
in the site-oriented approach one has to take into account correlations between
nearest-neighbour sites. Going beyond mean-field using the so-called
$n$-cluster approach our results for $\vm >1$ are in excellent agreement with
numerical simulations. We also present a modified cellular automaton which is
closely related to a two-dimensional dimer model.
