Let T be a (one-sorted first order) geometric theory (so T
has infinite models, T eliminates "there exist infinitely many" and
algebraic closure gives a pregeometry). I shall present some results
about T_P, the theory of lovely pairs of models of T as defined by
Berenstein and Vassiliev following earlier work of Ben-Yaacov, Pillay
and Vassiliev, of van den Dries and of Poizat. I shall present
results concerning superrosiness, the independence property and
imaginaries. As far as the independence property is concerned, I
shall discuss the relationship with recent work of Gunaydin and
Hieronymi and of Berenstein, Dolich and Onshuus. I shall also discuss
an application to Belegradek and Zilber's theory of the real field
with a subgroup of the unit circle. As far as imaginaries are
concerned, I shall discuss an application of one of the general
results to imaginaries in pairs of algebraically closed fields,
adding to Pillay's work on that subject.