Kagome fiber (KGF) is a new type of microstructure optical fiber, in which light guidance is not completely dependent on the photonic bandgap. This fiber displays some outstanding features such as flexible structure design, high damage threshold, low loss (as low as ~40 dB/km at high transmission wavelengths), and wide transmitting bandwidth (>500 nm). In particular, by adjusting the gas pressure in the fiber's hollow core, its nonlinearity and dispersion properties can be modulated easily for various important applications, including strong field physics, ultrafast nonlinear optics, and ultrashort pulse compression technology. In this paper we review the major experimental and theoretical progress achieved in recent years in KGF applications based on nonlinear optical frequency conversion and ultrashort pulse compression, then analyse the key technology behind their advanced applications. Finally, we assess the prospects for further applications of this novel fiber.