  The evolution of the star formation rate in the Galaxy is one of the key
ingredients quantifying the formation and determining the chemical and
luminosity evolution of galaxies. Many complementary methods exist to infer the
star formation history of the components of the Galaxy, from indirect methods
for analysis of low-precision data, to new exact analytic methods for analysis
of sufficiently high quality data. We summarise available general constraints
on star formation histories, showing that derived star formation rates are in
general comparable to those seen today. We then show how colour-magnitude
diagrams of volume- and absolute magnitude-limited samples of the solar
neighbourhood observed by Hipparcos may be analysed, using variational calculus
techniques, to reconstruct the local star formation history. The remarkable
accuracy of the data coupled to our maximum-likelihood variational method
allows objective quantification of the local star formation history with a time
resolution of ~ 50 Myr. Over the past 3Gyr, the solar neighbourhood star
formation rate has varied by a factor of ~ 4, with characteristic timescale
about 0.5Gyr, possibly triggered by interactions with spiral arms.
