Testosterone increases lean body mass and decreases fat mass in young men; the magnitude of the changes induced by testosterone in lean and fat mass are correlated with testosterone dose and the prevalent testosterone concentrations. Older men are as responsive to the anabolic effects of testosterone on the muscle as young men, but have increased frequency of adverse events with higher testosterone doses. This reciprocal change in lean and fat mass induced by androgens is best explained by the hypothesis that androgens promote the commitment of mesenchymal pluripotent cells into myogenic lineage and inhibit adipogenesis through an androgen receptor mediated pathway. Resident muscle satellite cells increase in number with testosterone administration forming myoblasts leading to greater numbers of myonuclei in larger myofibers. Testosterone administration is associated with increased size of motor neurons. The roles of 5-alpha reduction and aromatization of testosterone into dihydrotestosterone and estradiol, respectively, in mediating testosterone effects on body composition are poorly understood.
Though you may already be aware of potential side effects from testosterone abuse (note I said abuse and not use), here they are again: lowered HDL-cholesterol levels (good cholesterol), testicular atrophy, reductions in sperm count, prostate enlargement, liver damage (primarily with oral steroids that have been modified with a 17-alkyl substitution), menstrual irregularities, suppression of endogenous hormone levels (like LH and T), development of palpable breast tissue in men (also known as gynecomastia), clitoral enlargement, and acne.
The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.