You can follow along with progress in height-increasing research and new findings on the determinants of human height by using the “body height”[mh] search category on PubMed.
Right now, the only ways to increase height that I know of are:
1. limb-lengthening surgery (which is painful and has risks)
2. stretching exercises and lateral synovial joint loading (which only slightly increase height)
3. human growth hormone (which only increases height slightly at low doses, or has risks of side effects at high doses)
Advances in limb-lengthening implants with improved pain reduction will probably be the first techniques to increase height. Later, there could be techniques to increase height using stem cells and gene therapy. Here is a timeline of potential advances in increasing height.
Intermediate Height Increase:
1. Inducing microfractures while using analgesic medication or antinociceptive therapies to reduce pain
2. Having a limb-lengthening implant inserted
3. Using ultrasound, shock wave therapy, and electrical/electromagnetic stimulation to enhance bone formation
Advanced Height Increase:
1. Finding a way to reverse aging in bone and muscle by using gene therapy
2. Injecting mesenchymal stem cells to influence differentiation of bone and muscle cells
3. Reversing formation of growth plates in bones
4. Stimulating stem cells and the endocrine system to increase bone and muscle growth
The blog The Quest for Height shares excellent research on factors influencing human growth and height. I think the best way to increase height is to work with academic researchers who are willing to translate their research into work with humans. Techniques such as pellet implants that promote chondrogenesis will be promising, but these could take a while to become available for people. Experiments on increasing height with today’s technology would probably involve optimizing hormones, promoting expression of gene variants linked with height, and exploring joint loading.