Dental researchers are forging ahead with their branch of tissue engineering and regenerative medicine. It hasn't been long since engineered growth in situ of replacement teeth was demonstrated in rats, and now a research group has shown they can regenerate tooth enamel in mice, thereby healing cavities:
A new peptide, embedded in a soft gel or a thin, flexible film and placed next to a cavity, encourages cells inside teeth to regenerate in about a month ... The gel or thin film contains a peptide known as MSH, or melanocyte-stimulating hormone. Previous experiments [showed] that MSH encourages bone regeneration. Bone and teeth are fairly similar, so the French scientists reasoned that if the MSH were applied to teeth, it should help healing as well. To test their theory, the French scientists applied either a film or gel, both of which contained MSH, to cavity-filled mice teeth. After about one month, the cavities had disappeared.
You can also take a look at the research paper if interested, though it's fairly dense. It is an excellent example of what can be achieved where materials science meets biotechnology and the life sciences, and overall a very encouraging proof of concept. It is reasonable to expect, based on the progress of the past few years, that by the time those of us in middle age now begin to experience serious issues of wear and breakage with our dentistry, the technology to regenerate and regrow teeth will be well developed and widely available.
Fioretti, F., Mendoza-Palomares, C., Helms, M., Al Alam, D., Richert, L., Arntz, Y., Rinckenbach, S., Garnier, F., Haïkel, Y., Gangloff, S., & Benkirane-Jessel, N. (2010). Nanostructured Assemblies for Dental Application ACS Nano, 4 (6), 3277-3287 DOI: 10.1021/nn100713m