A novel form of biological control is being applied to the dengue virus. The agent is the maternally transmitted bacterium Wolbachia, naturally absent from the main dengue vector, the mosquito Aedes aegypti. Three Wolbachia-based control strategies have been proposed. One is suppression of mosquito populations by large-scale releases of males incompatible with native females; this intervention requires ongoing releases. The other interventions transform wild mosquito populations with Wolbachia that spread via the frequency-dependent fitness advantage of Wolbachia-infected females; those interventions potentially require just a single, local release for area-wide disease control. One of these latter strategies uses Wolbachia that shortens mosquito life, indirectly preventing viral maturation/transmission. The other strategy uses Wolbachia that block viral transmission. All interventions can be undermined by viral, bacterial or mosquito evolution; viral virulence in humans may also evolve. We examine existing theory, experiments and comparative evidence to motivate predictions about evolutionary outcomes. (i) The life-shortening strategy seems the most likely to be thwarted by evolution. (ii) Mosquito suppression has a reasonable chance of working locally, at least in the short term, but long-term success over large areas is challenging. (iii) Dengue blocking faces strong selection for viral resistance but may well persist indefinitely at some level. Virulence evolution is not mathematically predictable, but comparative data provide no precedent for Wolbachia increasing dengue virulence. On balance, our analysis suggests that the considerable possible benefits of these technologies outweigh the known negatives, but the actual risk is largely unknown.