Vision therapy is used to treat anything under the umbrella of binocular vision dysfunction. Convergence insufficiency is the most studied and most common of these conditions. Accommodative dysfunction and oculomotor dysfunction are also very common, and very treatable. These conditions almost invariably go hand in hand. Many cases of strabismus and amblyopia can also be improved with vision therapy. This is common Optometry school curriculum, and is taught to every graduating OD in the country, and is therefore within the purview of Optometry.
Indications for a binocular vision evaluation include: headaches/eye strain/double vision during visually demanding activities, lack of depth perception, cosmetic misalignment of the eyes, reduced visual acuity etc. An Optometrist should be more than capable of differentiating between cases which may be helped by vision therapy, or whether a different course of action is indicated such as a surgical referral, patching, change in glasses Rx, or whether the cause is pathological.
Visual perceptual difficulties are less easily measured, and not as well understood. I see no harm in attempting to improve these areas with currently available resources, as long as the patient understands what is being treated, and what isn't.
The article posted above about vision therapy quackery assumes false premises, so let me make them clear: There is no evidence that vision therapy treats learning disabilities, ADD, ADHD, Autism Spectrum Disorder, or any other behavioral problem, and those who make these claims are misrepresenting a relatively well-understood aspect of Optometry.
Optometrists who practice vision therapy are often referred to as developmental, or behavioral Optometrists. This can be a bit misleading, because we are not treating "behavioral issues" as most people understand them. We are using techniques which improve visual coordination in order to treat conditions such as the ones I've already listed.
More research is definitely needed. For those who condemn vision therapy because of the lack of gold standard studies, I would ask how much of commonly practiced medicine is actually backed by a randomized controlled trial. I think you'll find that if we were to eliminate all aspects of healthcare which are not backed by gold-standard research, there wouldn't be much left.
In the mean time, I will use the knowledge I have to treat the conditions I know how to treat. As an eye doctor, that is my responsibility. My patients will continue to benefit from my services, and I will continue to eliminate diplopia, visually-induced headaches, eye strain and fatigue, visual suppression, ocular motility/alignment, etc.
Without a good understanding of binocular dysfunction, a person is unlikely to understand the purpose and potential benefits of vision therapy. It's easy to dismiss a thing we know next to nothing about. So I challenge detractors to come up with an argument other than "not enough research, therefore quackery" and "you can't treat autism with vision therapy."
You may find this link to be somewhat helpful:
https://www.add-adhd.org/pdfs/03_sum_vt_research_Cooper.pdf