  The theory of evolution equations has been applied in various ways in general
relativity. Following some general considerations about this, some illustrative
examples of the use of ordinary differential equations in general relativity
are presented. After this recent applications of Fuchsian equations are
described, with particular attention to work on the structure of singularities
of solutions of the Einstein equations coupled to a massless scalar field. Next
the relations between analytical and numerical studies of the Einstein
equations are discussed. Finally an attempt is made to identify fruitful
directions for future research within the analytic approach to the study of the
Einstein equations.
