Once a beit din has ruled that a spouse is obligated to give the get (see #2 above) the beit din can publicize social sanctions against the get refuser.  If sanctions are not effective the beit din may conduct hearings to determine if the marriage can be voided (bitul kiddushin) without a get.  The status of the children of the marriage are not affected.  Marriages may be voided under certain conditions, such as, where the spouse is mentally dysfunctional, or homosexual, impotent, engages in domestic violence, or if the marriage ceremony itself was defective.