Abstract
Neutron stars are expected to have highly dense nuclear matter in their inner core region with density several times larger than usual atomic nuclei. In such highly dense matter, mesons and hyperons having the "strangeness " quantum number can appear as well as nucleons (neutrons and protons) and electrons. In this article, we give an overview of recent theoretical developments on phase transitions of normal neutron-star matter to a new phase including condensation of kaons, the lightest mesons having the strangeness. We consider coexistence of kaon condensation and hyperons in highly dense matter and discuss the effects of the kaon-condensed phase in hyperonic matter on the internal structure of neutron stars such as mass-radius relations. In particular, a possible existence of self-bound objects with kaon condensates and hyperons on any scale is suggested.