Metric-like Lagrangian formulations for higher-spin fields of mixed symmetry

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting extending the metric formulation of linearized gravity, and then the (γ-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.