Nonlinear propagation of intense femtosecond laser pulses in bulk transparent media leads to a specific propagation regime, termed femtosecond filamentation, which in turn produces dramatic spectral broadening, or superbroadening, termed supercontinuum generation. Femtosecond supercontinuum generation in transparent solids represents a compact, efficient and alignment-insensitive technique for generation of coherent broadband radiation at various parts of the optical spectrum, which finds numerous applications in diverse fields of modern ultrafast science. During recent years, this research field has reached a high level of maturity, both in understanding of the underlying physics and in achievement of exciting practical results. In this paper we overview the state-of-the-art femtosecond supercontinuum generation in various transparent solid-state media, ranging from wide-bandgap dielectrics to semiconductor materials and in various parts of the optical spectrum, from the ultraviolet to the mid-infrared spectral range. A particular emphasis is given to the most recent experimental developments: multioctave supercontinuum generation with pumping in the mid-infrared spectral range, spectral control, power and energy scaling of broadband radiation and the development of simple, flexible and robust pulse compression techniques, which deliver few optical cycle pulses and which could be readily implemented in a variety of modern ultrafast laser systems. [ABSTRACT FROM AUTHOR]