We review the physical properties, linear and nonlinear optical characteristics, and phase-matching configurations of BiB3O6 (BIBO), the first low-symmetry (monoclinic) inorganic nonlinear crystal that has found broad applications for frequency conversion of laser sources from the UV, across the visible, to the near-IR based on three-wave interactions. We describe in detail the most relevant optical properties that make this material an attractive candidate for nonlinear frequency conversion of laser light in general, and ultrafast femtosecond laser sources in particular. With special focus on ultrafast frequency conversion, characteristics such as group-velocity mismatch and spectral acceptance, parametric gain bandwidth, group-velocity dispersion, as well as angular acceptance and spatial walk-off are evaluated and optimum configurations for the attainment of maximum conversion efficiency, minimum pulse duration, and highest spatial beam quality are identified and compared with the most widely established alternative borate crystal, beta-BaB2O4. Experimental results are presented on both parametric up- and down-conversion of femtosecond pulses, from the high-energy, low-repetition-rate (1 kHz) to the low-energy, high-repetition-rate (56-76 MHz) regime, demonstrating the unique versatility of BIBO for efficient frequency conversion of femtosecond pulses with broad tunability from 250 nm in the UV, throughout the visible, up to sim 3000 nm in the IR.