This article offers an extensive survey of results obtained using hybrid photonic crystal fibers (PCFs) which constitute one of the most active research fields in contemporary fiber optics. The ability to integrate novel and functional materials in solid- and hollow-core PCFs through various post-processing methods has enabled new directions towards understanding fundamental linear and nonlinear phenomena as well as novel application aspects, within the fields of optoelectronics, material and laser science, remote sensing and spectroscopy. Here the recent progress in the field of hybrid PCFs is reviewed from scientific and technological perspectives, focusing on how different fluids, solids and gases can significantly extend the functionality of PCFs. In the first part of this review we discuss the most important efforts by research groups around the globe to develop tunable linear and nonlinear fiber-optic devices using PCFs infiltrated with various liquids, glasses, semiconductors and metals. The second part is concentrated on the most recent and state-of-the-art advances in the field of gas-filled hollow-core PCFs. Extreme ultrafast gas-based nonlinear optics towards light generation in the extreme wavelength regions of vacuum ultraviolet (VUV), pulse propagation and compression dynamics in both atomic and molecular gases, and novel soliton - plasma interactions are reviewed. A discussion of future prospects and directions is also included.