  The simultaneous presence of two competing inter-particle interactions can
lead to the emergence of new phenomena in a many-body system. Among others,
such effects are expected in dipolar Bose-Einstein condensates, subject to
dipole-dipole interaction and short-range repulsion. Magnetic quantum gases and
in particular Dysprosium gases, offering a comparable short-range contact and a
long-range dipolar interaction energy, remarkably exhibit such emergent
phenomena. In addition an effective cancellation of mean-field effects of the
two interactions results in a pronounced importance of quantum-mechanical
beyond mean-field effects. For a weakly-dominant dipolar interaction the
striking consequence is the existence of a new state of matter equilibrated by
the balance between weak mean-field attraction and beyond mean-field repulsion.
Though exemplified here in the case of dipolar Bose gases, this state of matter
should appear also with other microscopic interactions types, provided a
competition results in an effective cancellation of the total mean-field. The
macroscopic state takes the form of so-called quantum droplets. We present the
effects of a long-range dipolar interaction between these droplets.
