  We use the Millennium Simulation, and an abundance-matching framework, to
investigate the dynamical behaviour of galaxy pairs embedded in a cosmological
context. Our main galaxy-pair sample, selected to have separations under 250
kpc/h, consists of over 1.3 million pairs at redshift z = 0, with stellar
masses greater than 10^9 Msun, probing mass ratios down to 1:1000. We use dark
matter halo membership and energy to classify our galaxy pairs. In terms of
halo membership, central-satellite pairs tend to be in isolation (in relation
to external more massive galaxies), are energetically- bound to each other, and
are also weakly-bound to a neighbouring massive galaxy. Satellite-satellite
pairs, instead, inhabit regions in close proximity to a more massive galaxy,
are energetically-unbound, and are often bound to that neighbour. We find that
60% of our paired galaxies are bound to both their companion and to a third
external object. Moreover, only 9% of our pairs resemble the kind of systems
described by idealised binary merger simulations in complete isolation. In sum,
we demonstrate the importance of properly connecting galaxy pairs to the rest
of the Universe.

Cosmology and Nongalactic Astrophysics