Summary: Let \(\Omega \subset\mathbb{R}^3\) be an open set. We study the spectral properties of the free Dirac operator \(\mathcal{H} :=- i \alpha \cdot \nabla + m\beta\) coupled with the singular potential \(V_{\kappa} =(\epsilon I_4 +\mu \beta + \eta (\alpha \cdot N))\delta_{\partial \Omega} \), where \(\kappa =(\epsilon, \mu, \eta)\in\mathbb{R}^3\). The open set \(\Omega\) can be either a \(\mathcal{C}^2\)-bounded domain or a locally deformed half-space. In both cases, self-adjointness is proved and several spectral properties are given. In particular, we give a complete description of the essential spectrum of \(\mathcal{H} + V_{\kappa}\) in the case of a locally deformed half-space, for the so-called critical combinations of coupling constants. Finally, we introduce a new model of Dirac operators with \(\delta\)-interactions and deal with its spectral properties. More precisely, we study the coupling \(\mathcal{H}_{\zeta, \upsilon} =\mathcal{H}+ \left( -i\zeta \alpha_1\alpha_2\alpha_3 + i\upsilon \beta \left( \alpha\cdot N\right) \right) \delta_{\partial \Omega}\), with \(\zeta, \upsilon \in\mathbb{R}\). In particular, we show that \(\mathcal{H}_{0,\pm 2}\) is essentially self-adjoint and generates confinement.