Fluorescent nanodiamonds made from high-pressure high-temperature diamond are increasingly used in biological imaging and sensing applications. To date, only red and green fluorescent nanodiamonds are widely available, severely limiting nanodiamond-based multiplexed imaging. Here, we report on recent progress in the fabrication and characterization of fluorescent nanodiamonds with fluorescence colors from 450 nm to 900 nm. The fluorescence originates from a range of fluorescent color centers based on nitrogen, silicon, nickel and vacancy defects in the diamond lattice. The optical properties of these color centers in diamond nanoparticles are discussed in detail and the utility of nanodiamond-based multiplexed bioimaging demonstrated in experiments in-vitro.