  Observations suggest, that there may be periods in the history of the
universe, including the present one, in which its evolution is driven by scalar
fields. This paper is concerned with the solution of the evolution equations
for a spatially flat universe driven by a single scalar field. Some general
theorems relevant to the cosmology of these models are presented, and several
approaches to solve the equations are discussed. For some potentials special
exact solutions can be found, and for the case of exponential potentials the
complete solution is rederived in a new parametrization. For the general case
solutions are constructed in terms of a power series expansion in the field.
The issue of double-valuedness of such a series expansion in case of
oscillating fields with turning points is addressed and resolved.
