This Thesis discusses various Lagrangian formulations of the free theory of massless higher-spin fields of mixed symmetry. These are tensors (or spinor-tensors) with several groups of symmetrised indices, and allow one to describe in a covariant fashion the representations of the Poincaré group labelled by multi-row Young tableaux. They appear when the dimension of space-time is bigger than four and are ubiquitous in the spectra of String models. The goal of providing tools for the comparison between String Theory and Higher Spin Gauge Theories is indeed an important motivation for the work reviewed in the Thesis. A metric-like Lagrangian for arbitrary mixed-symmetry bosons was already proposed by Labastida in the mid Eighties in terms of fields subject to suitable trace constraints. On the contrary, a Lagrangian for arbitrary mixed-symmetry fermions was not available neither in a metric nor in a frame-like setup (where the degrees of freedom are encoded in sets of differential forms rather than in multi-symmetric tensors). The main original results in this Thesis are therefore the first Lagrangian altogether for mixed-symmetry fermions and a Lagrangian for mixed-symmetry bosons involving a number of unconstrained fields that only depends on the number of rows in the associated Young tableau. Both results have been obtained in collaboration with D. Francia, J. Mourad and A. Sagnotti. For fermions the Thesis presents both a constrained formulation along the lines of the work by Labastida and an unconstrained one, again with a number of fields that only depends on the number of rows in the Young tableau. The advantages of the latter are the easier comparison with String Field Theory and the chance to recover a Lagrangian expressed in terms of higher-spin curvatures by integrating over the auxiliary fields. In analogy with two-dimensional gravity, the proposed Lagrangians display additional Weyl-like gauge symmetries in space-time dimensions where they do not propagate local degrees of freedom. Various examples and a partial classification of these previously unnoticed cases are also discussed in the Thesis.