  Fragmentation and fission of giant molecular clouds occasionally results in a
pair of gravitationally bound star clusters that orbit their mutual centre of
mass for some time, under the influence of internal and external perturbations.
We investigate the evolution of binary star clusters with different orbital
configurations, with a particular focus on the Galactic tidal field. We carry
out $N$-body simulations of evolving binary star clusters and compare our
results with estimates from our semi-analytic model. The latter accounts for
mass loss due to stellar evolution and two-body relaxation, and for evolution
due to external tides. Using the semi-analytic model we predict the long-term
evolution for a wide range of initial conditions. It accurately describes the
global evolution of such systems, until the moment when a cluster merger is
imminent. $N$-body simulations are used to test our semi-analytic model and
also to study additional features of evolving binary clusters, such as the
kinematics of stars, global cluster rotation, evaporation rates, and the
cluster merger process. We find that the initial orientation of a binary star
cluster with respect to the Galactic field, and also the initial orbital phase,
are crucial for its fate. Depending on these properties, the binaries may
experience orbital reversal, spiral-in, or vertical oscillation about the
Galactic plane before they actually merge at $t\approx100$~Myr, and produce
rotating star clusters with slightly higher evaporation rates. The merger
process of a binary cluster induces an outburst that ejects $\sim10\%$ of the
stellar members into the Galactic field.
