  We present an overview of our recent investigations of long-range
interactions in an ultracold Cs Rydberg gas. These interactions are studied by
high-resolution photoassociation spectroscopy, using excitation close to
one-photon transitions into $n$p$_{3/2}$ Rydberg states with pulsed and
continuous-wave ultraviolet laser radiation, and lead to the formation of
long-range Cs$_2$ molecules. We observe two types of molecular resonances. The
first type originates from the correlated excitation of two atoms into
Rydberg-atom-pair states interacting at long range via multipole-multipole
interactions. The second type results from the interaction of one atom excited
to a Rydberg state with one atom in the electronic ground state. Which type of
resonances is observed in the experiments depends on the laser intensity and
frequency and on the pulse sequences used to prepare the Rydberg states. We
obtain insights into both types of molecular resonances by modelling the
interaction potentials, using a multipole expansion of the long-range
interaction for the first type of resonances and a Fermi-contact
pseudo-potential for the second type of resonances. We analyse the relation of
these long-range molecular resonances to molecular Rydberg states and ion-pair
states, and discuss their decay channels into atomic and molecular ions. In
experiments carried out with a two-colour two-photon excitation scheme, we
observe a large enhancement of Rydberg-excitation probability, which we
interpret as a saturable autocatalytic antiblockade phenomenon.
