The dissertation contains a discussion of research results on shaping selected properties of micro- and nanostructured specialty optical fibers dedicated to applications in fiber-based ultrashort pulse laser systems. The research was conducted in the context of application of specialty optical fibers in coherently seeded ultrafast fiber amplifiers. Two types of optical fibers were the research subject, distinguished based on their roles in fiber amplifier systems. The first one is related to structured optical fibers for a coherent white light pulse generation, i.e., the supercontinuum. The goal was to develop optical fiber structures exhibiting high χ(3) nonlinearity, flat chromatic all-normal dispersion characteristics, and strong birefringence. The second type of the investigated fibers refers to the anti-resonant hollow-core fibers. The aim here was the development and experimental characterization of such fibers for enabling transmission of broadband, ultrashort laser pulses, with minimized spectro-temporal distortion caused by dispersion or nonlinear effects. Therefore, the described research relates to studying the propagation of electromagnetic waves in dielectric media, in the presence of a strong spatial confinement in a plane transverse to the propagation direction and over distances vastly exceeding the transverse dimensions of these media. In the first part of the dissertation, all-glass, all-normal dispersion, and highly nonlinear structured optical fibers are described. The chapter contains the results of designing, fabrication, and experimental characterization of such fibers. As demonstrated, the fibers' optical nonlinearity enables the generation of full-octave spectrally broadened optical pulses entirely in the normal dispersion wavelength range. The generation process is stimulated by femtosecond laser pulses with peak powers not exceeding several tens of kilowatts. Pulses are generated by compact mode-locked fiber lasers at repetition rates not lower than several tens of MHz. This approach allows for a direct seeding of continuous-wave pumped fiber amplifiers. However, since such sources have a limited peak power, the analysis is concentrated on soft-glass fiber structures with a high nonlinear refractive index. In the research work scope, in-house numerical tools for structured fiber designing were developed based on the finite element method. The numerical tools allow for the inclusion of the impact of structure drawing thermal process at the fiber drawing tower on the distribution of the structure's refractive index. A discussion of group birefringence and chromatic dispersion measurement results is also provided. The second part of the work is devoted to studies of the possibility of fiber nonlinearity control by the polarization of the in-coupled light. In particular, the work involves an optical fiber with nanostructured core forming an artificially anisotropic optical medium. A comparison between soft-glass and silica glass-based structures is provided with a discussion of both approaches' advantages and drawbacks. The research methodology embraces elaboration of own tools for numerical simulations of the fiber's nonlinear coefficient values and a detailed analysis of the polarization-dependent distribution of mode field guided in the fiber's nanostructured core. Technological aspects of the fabrication feasibility of such a fiber structure is also discussed. The third part of the dissertation includes results on numerical simulation and experimental characterization of linear and nonlinear properties of anti-resonant hollow-core fibers. Due to light guidance in a hollow core and a small overlap of the guided mode with glassy cladding elements, anti-resonant fibers offer a large number of interesting transmission properties. Among others, it is possible to obtain an ultrashort pulse transmission with negligible nonlinear or dispersion distortion. The presented results contain comprehensive studies on designing a standard and birefringent structure of anti-resonant hollow-core fibers for wavelength ranges covering mature laser and ultrafast fiber amplifier systems. Moreover, the spectro-temporal characterization of the ultrashort pulse transmitted in such fibers is presented and discussed.