In this PhD thesis we investigate various aspects of particle dark matter. The proper identification of dark matter developed during the second half of the twentieth century to become one of the biggest endeavours in modern physics and astronomy. Although observations currently favour the explanation that dark matter consists of a new form of particle, no experimental search has yet provided unequivocal evidence of such a particle. Of particular importance in this thesis is the field of indirect detection of dark matter, where one searches for the particles emerging from annihilations of dark matter particles out in the Universe. Specifically, we consider dark matter annihilations in the centre of the Sun. As the Sun moves through the gala...