In this thesis, previous research on discontinuity geometry, in-situ block size distribution (IBSD), blasted block size distribution (BBSD), and blastability of rock mass is discussed. The IBSD with special reference to discontinuities with a fractal spacing distribution is investigated using computer simulation, from which a set of empirical equations is derived for predicting the IBSD of a rock mass with discontinuities of fractal spacing distributions. The goodness-of-fit of theoretical as compared with real spacing distributions is discussed and a grey correlation analysis technique is introduced into the goodness-of-fit. An estimation of mean trace length of discontinuities with lognormal and fractal distributions is derived. A numerical algorithm and associated computer program for estimating the discontinuity size distribution is developed from which empirical equations for estimating the mean size of discontinuities with negative exponential, lognormal and fractal trace length distributions have been derived. A factor which accounts for the discontinuity impersistence is incorporated into the estimation of IBSD. Combining both Ross-Ram and Schuhmann models, a reasonably accurate and user-friendly "photo-scanline" technique is devised for the estimation of BBSD of the blastpile. Blasting results, as a function of both the intact rock properties and the discontinuity structures are investigated, and an energy-block-transition model characterising the blastability of rock masses is developed. It is argued that the blastability of rock mass is governed by a comprehensive range of both intact rock properties and discontinuity parameters, and that the fractal dimension of the IBSD of a rock mass could be an indicator of blastability. Taking into account that blastability is a complex property, a methodology of assessing blastability of rock masses is introduced using a Rock Engineering Systems method. Published data from the literature has been used wherever possible to support the validation of the new techniques of analysis and two case histories in which applications of the developed methodologies and techniques are presented.