Disk galaxies are complex systems where stars, gas, and dust evolve within dark matter halos through gravitational interactions. Among their most prominent features are bars and spiral arms, whose formation and structure are shaped by nonlinear dynamical processes. Observational data, theoretical orbital studies using analytic potentials, and fully self-consistent N-body simulations collectively indicate that the spiral arms are mainly two-dimensional structures. On the other hand, bars comprise two structural elements: an elongated outer “slim” region and a more compact, vertically extended central “thick” component. To gain insight into how these structures form and persist, we examine the nature of stellar orbits within galactic disks. The orbital behavior in both two- and three-dimensional Hamiltonian systems that model rotating barred potentials provides the foundation for interpreting the observed morphologies of barred-spiral galaxies. Due to the strong departure from axisymmetry introduced by bars and spirals, nonlinear dynamical processes are essential in understanding their evolution. Stellar orbits provide the key to understanding these features. Two-dimensional (2D) orbital models help explain the dynamics of spiral arms and outer bars, where both regular and chaotic orbits may play structural roles. However, to explore the vertically extended, central “thick” parts of bars—often observed as boxy or peanut-shaped (b/p) bulges in edge-on galaxies—three-dimensional (3D) models are essential. These bulges are supported by specific 3D families of periodic orbits that bifurcate from the central planar x1 family at vertical resonances. Although many of these families exhibit complex instability, orbits in their vicinity can still contribute to building the vertical structure, especially through sticky behavior in phase space. This talk will present the key orbital mechanisms supporting bars and spirals, with a focus on how certain orbit families shape b/p bulges and the characteristic X-shaped structures embedded within them.