One of the most important issues for the design of filament-wound pressure vessels reflects on the determination of the most efficient meridian profiles and related fiber architectures, leading to optimal structural performance. To better understand the design and optimization of filament-wound pressure vessels, in this dissertation we present an overview and comprehensive treatment for toroidal and domed pressure vessels. Since the geodesic winding has severe boundary conditions that confine the layup optimization, the non-geodesic trajectories are here extensively applied to enlarge the design space. Designing optimal laminate layup is not the only issue; the fibers must be stable on the mandrel and be exactly placed along trajectories as predetermined by structural design. To obtain a stable fiber trajectory, the stability-ensuring conditions are formulated in terms of both fiber slippage and bridging tendencies; these conditions provide the basic criteria for the subsequent design of various pressure vessels. The mathematical description of the geodesics and non-geodesics on a generic shell of revolution is briefly presented. A generalized optimality criterion that is adapted to various optimal design problems for pressure vessels is elaborated. This condition originates from the idea that the optimal pressure vessels are governed by the condition of equal shell strains, or equivalently, zero shear stress at lamina level. The specific equations and the feasible intervals of the optimality condition are also given for several types of laminations. The basic equations of the netting analysis and their applications to the design of circular toroidal pressure vessels are here outlined. The influence of the fiber layup and the geometry of the toroid on the stability of netting-dictated fiber trajectories are evaluated. A new possibility to improve the vessel performance can be offered by the application of adapted cross-sectional shapes instead of the conventional shapes. The isotensoid design, which leads to equal fiber tension throughout the whole structure, is conducted to determine the netting-based optimal cross-sectional shapes. The governing equations for determining geodesic and non-geodesic isotensoids are respectively derived and their feasible intervals are also determined. In addition, a simplified method for designing isotensoid pressure vessels with unequal polar opening is also outlined, with the aid of non-geodesic trajectories. The optimal design, based on orthotropic plate theory, is divided into two basic approaches: numerical and semi-analytical methods. A numerical optimization method is specially designed for determining the optimal meridian profiles of bellow-shaped pressure vessels. An integral design method is proposed for circular toroidal pressure vessels, with emphasis on the determination of the optimal non-geodesic trajectories and winding patterns. Based on the previously-obtained (generalized) optimality condition, semi-analytical design methods are presented for the determination of the optimal meridian profiles for continuum-based domes and toroids, respectively. The optimal cross sectional shapes lead to significantly improved vessel performance. An extensive study of the manufacturing of filament wound toroidal pressure vessels is conducted. We here emphasize the importance of suitable winding patterns for obtaining an optimal pressure vessel, and we accordingly derived the "Diophantine"-alike pattern equations that produced such patterns. The main objective of the method presented here is to match the structure-dictated number of wound circuits to the solution of the pattern equations for determining the proper winding velocities of the mandrel and the feed eye. In addition, depending on the aimed lathe machine configuration, the underlying geometric model of the new-fashioned toroidal winder is outlined and the kinematic solutions for coupling the motion of the mandrel and the feed eye are also given. Simulations of geodesic and non-geodesic trajectories are performed for winding toroidal pressure vessels. Last but not least, since ultra-high pressure vessels require thick-walled designs, this dissertation is also extended to three-dimensional problems where the through-thickness stress gradient is taken into account. A three-dimensional (3D) elasticity analysis on multi-layered thick-walled pressure vessels is here addressed. In order to better understand the design approaches of thick-walled composite cylinders and find ways to improve their structural performance, a review is devoted to 3D elasticity approaches for obtaining the exact solutions of the stresses and strains induced by internal pressure, and the effects of hygrothermal loading and twisting. The 3D effective elastic constants and most frequently used failure criteria for cylindrically anisotropic materials are also presented.