So I only remembered a little bit of the virology of phages from what I learned in school--namely, that they infect bacteria and that they are everywhere. And when I saw some of the early comments posted here that were big on knee-jerk reactions and scarcasm but small on actual science, I decided to read the Wikipedia article.
Phages don't infect eukaryotes; they only infect bacteria. And phage therapy has been successfully used to combat antibiotic resistance in humans, although the problem of resistance in general remains. This makes sense: bacteria replicate rapidly and have relatively little in the way of proofreading mechanisms, so when there is selection pressure, they mutate and develop resistance very easily, even to phages. So engineering a phage to target an antibiotic-resistant bacterial strain might work in the short term, but unless there's a way to cultivate phages that are able to adapt in response to (and not simply target) that strain, the strategy is intrinsically self-limiting.
To those comments drawing ill-informed comparisons to engineering viruses that infect humans, know this: phages are literally everywhere on this planet. They are far, far more abundant than bacteria, and most people can appreciate how ubiquitous bacteria are. You already have phages inside of you, and in fact, they form an entire ecosystem. Same thing with bacteria--you have bacteria all over and inside your body. You have more bacterial cells coexisting on and inside you than you have your own cells. And what's more interesting is that these phages seem to be protective by helping to maintain a balanced microbiome.
The concern I have with engineered phages is not that they would be harmful to the environment or to us, or that they could mutate to be harmful. That is extremely, extremely unlikely, because such a concern doesn't reflect an understanding of how phages actually function in real life and how they co-evolve with the bacteria they infect. If anything I would be concerned about spreading bacteria that become extensively resistant to antibiotics and phages. Thus we need better education about what phage therapy is, and to ensure that study participants are adequately informed of the potential risks and benefits. The direction such therapy would most likely need to take is quite similar to CRISPR and other gene therapies, in that it would need to be a form of personalized medicine. If we can develop computer models to help perform this personalization more efficiently, then I'm for it; such an approach may also prove useful for treating cancer.