A variety of configurations for suture tie devices and suture tie device applicators, as well as methods of suturing, are disclosed. The suture tie devices generally include at least one leg member having a curved or angled distal, tissue engaging portion. A tying member unidirectionally or bidirectionally displaceable along the leg member can optionally be provided. Engagement of a leg distal portion with a generally opposed leg distal portion or the tying member forms a suture loop which positions organ or tissue material between the curved or angled legs and the tying member. The tying member can be advanced toward the leg member so as to provide a variable extent of suture tension. Apparatus for installing the suture tie devices and suturing methods are also disclosed.