The higher spin theory is the field of theoretical physics at the center of this thesis. Besides an introduction presenting the general context of the birth of this theory, this PhD thesis consists of three recent studies in this area. Particular attention will be paid to symmetries, currents and holography. The first part focuses on the ingredients for the construction of cubic vertices between a scalar matter field and a higher spin gauge field in a constant curvature space-time. Noether's method describes how to build the interactions from conserved currents, whose writing may be condensed using generating functions. Ambient formalism is the main aspect of this calculation since it allows simplification. In a second step, we prepare the around for a future test of the holographic correspon- dence in the cubic or quartic order in the coupling constant. More specifically, we review in detail the computation of some propagators, which leads us to calculate three-point functions involving two scalar fields. The last part, although always on the higher spin holography, deals with non-relativistic physics. Symmetries and currents of an ideal or unitary Fermi gas are studied. In particular, we prove that the maximal symmetry algebra of Schrödinger equation is the Weyl alge- bra. The link between relativistic and non-relativistic physics is obtained by Bargmann's dimensional reduction. The higher spin nonrelativistic holography is also discussed.
