  Efimov physics is drastically affected by the change of spatial dimensions.
Efimov states occur in a tridimensional (3D) environment, but disappear in two
(2D) and one (1D) dimensions. In this paper, dedicated to the memory of Prof.
Faddeev, we will review some recent theoretical advances related to the effect
of dimensionality in the Efimov phenomenon considering three-boson systems
interacting by a zero-range potential. We will start with a very ideal case
with no physical scales, passing to a system with finite energies in the
Born-Oppenheimer (BO) approximation and finishing with a general system. The
physical reason for the appearance of the Efimov effect is given essentially by
two reasons which can be revealed by the BO approximation - the form of the
effective potential is proportional to $1/R^2$ ($R$ is the relative distance
between the heavy particles) and its strength is smaller than the critical
value given by $-(D-2)^2/4$, where $D$ is the effective dimension.
