  Analogue gravity is based on the simple observation that perturbations
propagating in several physical systems can be described by a quantum field
theory in a curved spacetime. While phenomena like Hawking radiation are hardly
detectable in astrophysical black holes, these effects may be experimentally
tested in analogue systems. In this Thesis, focusing on Bose-Einstein
condensates, we present our recent results about analogue models of gravity
from three main perspectives: as laboratory tests of quantum field theory in
curved spacetime, for the techniques that they provide to address various
issues in general relativity, and as toy models of quantum gravity. The
robustness of Hawking-like particle creation is investigated in flows with a
single black hole horizon. Furthermore, we find that condensates with two
(white and black) horizons develop a dynamical instability known in general
relativity as black hole laser effect. Using techniques borrowed from analogue
gravity, we also show that warp drives, which are general relativistic
spacetimes allowing faster-than-light travel, are unstable. Finally, the
cosmological constant issue is investigated from an analogue gravity
perspective and relativistic Bose-Einstein condensates are proposed as new
analogue systems with novel interesting properties.
