Fiber delivery of intense laser radiation is important for a broad range of application sectors, from medicine through to industrial laser processing of materials, and offers many practical system design and usage benefits relative to free space solutions. Optical fibers for high power transmission applications need to offer low optical nonlinearity and high damage thresholds. Single-mode guidance is also often a fundamental requirement for the many applications in which good beam quality is critical. In recent years, microstructured fiber technology has revolutionized the dynamic field of optical fibers, bringing with them a wide range of novel optical properties. These fibers, in which the cladding region is peppered with many small air holes, are separated into two distinct categories, defined by the way in which they guide light: (1) index-guiding holey fibers (HFs), in which the core is solid and light is guided by a modified form of total internal reflection, and (2) photonic band-gap fibers (PBGFs) in which guidance in a hollow core can be achieved via photonic band-gap effects. Both of these microstructured fiber types offer attractive qualities for beam delivery applications. For example, using HF technology, large-mode-area, pure silica fibers with robust single-mode guidance over broad wavelength ranges can be routinely fabricated. In addition, the ability to guide light in an air-core within PBGFs presents obvious power handling advantages. In this paper we review the fundamentals and current status of high power, high brightness, beam delivery in HFs and PBGFs, and speculate as to future prospects.