There is a "white light initiative" that seeks to develop efficient white LED's. This research is ongoing and has reported limited success. As Rich2001 indicated, one strategy is to use a filter, which is not too efficient. Another strategy is to use particular wavelengths of light, which, when combined, produce white light. This is much more efficient, but presents a major challenge with today's technology. If efficient white LED's are successfully produced, there is little doubt that they will eventually replace the common filament light bulb. However, it will probably take some time, given that existing light sockets would almost certainly require replacement to accomodate LEDs.