Over the last decade, genetically modified crops have become widespread in agriculture. One of the more successful of these are Bt crops - transgenic plants that express genes derived from Bacillus thuringensis. These genes allow the plants to produce toxins which specifically affect certain groups of insects. Since these plants do not need to be sprayed, and since the toxins are relatively specific, the environmental effects appear to be lower than conventional agriculture.
However, Bt toxins face the same problem that other pesticides face - the evolution of resistance in target insects. The selective pressure of a compound in your food that kills you (unless you have a resistance gene) is huge. The more widely a Bt crop is planted, the greater the selective pressure. And unlike pesticides, to which a pest is only exposed periodically, Bt toxins will (presumably) be produced by the plants on a continuous basis. Since lab studies had showed that pest species possessed genetic variation in their resistance to Bt toxins (including this 1998 EPA study), the question is more one of how quickly resistance would evolve, rather than if resistance would evolve.
One strategy to slow the evolution of resistance is to plant areas of non-Bt plants near to the fields of Bt crops. These would serve as refuges for populations of non-resistant insects. In principle it should work great - as long as the resistance genes are recessive. If you plant a large area of crops that are toxic to their pests, what happens is that most of the pest population will be wiped out. A few will have some resistance (after all, Bt toxins exist in nature - Bacillus thuringensis occurs in nature, and is likely to have interacted with the pest species in its evolutionary history). Since all the individuals lacking resistance genes would have been knocked out of the population, resistant individuals would mate with one-another. As a result, each subsequent generation should be more resistant than the previous. However, if you provide a refuge of non-Bt crops, most of the individuals in the next generation would come from that part of the population.
If resistance to Bt toxin is a recessive trait, an individual needs to inherit the gene from both parents in order to be resistant. If the population is only made up of those who survived exposure to the toxin, they will mate with one-another, and their offspring will inherit the trait. On the other hand, if the population is dominated by susceptible individuals (those that fed on the non-Bt crop) then the survivors’ genes will be diluted in a much larger population. On the other hand, if resistance is a dominant trait, providing a refuge won’t work. If the trait is dominant, it doesn’t matter who the survivors mate with - they will still be able to pass their resistance on to their offspring.
In an article published in Nature Biotechnology, Bruce Tabashnik and colleagues looked at the actual pattern of evolution of resistance to Bt toxin Cry1Ac in cotton over a 10-year period. They used studies conducted in Australia, China, Spain and the United States focusing on six pest species: Helicoverpa armigera, H. zea, Heliothis virescens, Ostrinia nubilalis, Pectinophora gossypiella and Sesamia nonagrioides. They found that in only one of these species - H. zea - had the frequency of resistance genes increased substantially.
One explanation for the evolution of resistance in H. zea is the observation that resistance to the Bt toxin Cry1Ac appears to be the dominant trait. This greatly reduces the effectiveness of refuges, since the resistance genes aren’t diluted out as effectively as they would be if they were recessive.
Helicoverpa zea has not evolved resistance in all areas - populations in Arkansas and Mississippi had done so, but those in North Carolina had not. This was attributed to differences in the effective refuge sizes:
Gustafson et al.  meticulously estimated that the effective refuge abundance during each of three generations when H. zea fed on cotton was 39% in Arkansas and Mississippi and 82% in North Carolina. With these refuge sizes, H. zea is projected to evolve resistance after 9 years in Arkansas and Mississippi. By contrast, in North Carolina, resistance evolution should take >20 years, with the expected resistance allele frequency still <0.005 after 10 years.
However, the evolution of resistance has not led to any crop failures. Even where resistance has evolved, most populations are not resistant, and even among resistant strains “Cry1Ac in Bt cotton still caused 48–60% larval mortality”. In addition, spraying is still used to combat large pest outbreaks, and “pyramided” transgenic plants which contain both Cry1Ac and a second Bt toxin, Cry2Ab have been introduced. Resistance to one Bt toxin does not convey resistance to the other, so it’s far more difficult for pests to evolve resistance to plants producing both toxins.
Tabashnik, B.E., Gassmann, A.J., Crowder, D.W., Carriére, Y. (2008). Insect resistance to Bt crops: evidence versus theory. Nature Biotechnology, 26(2), 199-202. DOI: 10.1038/nbt1382