Though it came to be fashionable in the last decade research is lacking. I am not saying it doesn't have a place, but one should be careful.
Have a look:
Treatment of Men for “Low Testosterone”: A Systematic Review
Studies that examined clinical effects have not favored testosterone therapy over placebo. Two of 3 studies that assessed angina showed no effect. Three studies from the same group found a benefit for symptoms associated with CHF. One study was stopped early for cardiovascular adverse effects.
Testosterone supplementation did not demonstrate consistent effectiveness for improving sexual function or satisfaction. Testosterone is ineffective in treating ED. Controlled trials were mixed on libido, with more positive than negative studies.
Substantial evidence supports a favorable effect of testosterone treatment on muscle mass in both healthy men and men with HIV, and a majority of studies showed a decrease in fat mass. Testosterone did not affect most measures of muscle strength. While decreasing frailty and increasing strength in older men might be beneficial, testosterone supplementation does not improve physical function in older men.
Most studies on mood-related endpoints found no beneficial effect of testosterone treatment on personality, psychological well-being, or mood. Although 2 studies showed decreased anxiety, treatment of depression showed mixed and inconsistent results. Even if testosterone did benefit mood, social adverse events might ensue; 5 studies noted treatment-related increases in anger, aggression, or hostility. Testosterone did not benefit cognitive impairment or Alzheimer disease; neither did it benefit verbal fluency, memory, or other cognitive endpoints in normal men.
In summary, evidence from RCTs does not support treatment of so-called low-T for improving physical function, sexual function, mood, or cognition. Testosterone increases muscle mass, but not strength, and while some improvement is seen in some surrogate markers of cardiovascular risk, there is little evidence of clinical benefit.
However, and his is a big however, there may be a good reason for the lack of effects in standardised trials. Testosterone (like steroids in general) is often considered a magic pill. However, without other adjustments, like exercise, diet, sleep etc. it may not be sufficient on its own to produce results. I also wonder about the methodology of some studies: I find it hard to believe that testosterone enanthate at 600 mg a week (as they used in one of the studies) did not result in improved physical strength.