Methods and systems for closing an opening or defect in tissue, closing a lumen or tubular structure, cinching or remodeling a cavity or repairing a valve preferably utilizing a purse string or elastic device. The preferred devices and methods are directed toward catheter-based percutaneous, transvascular techniques used to facilitate placement of the devices within lumens, such as blood vessels, or on or within the heart to perform structural defect repair, such as valvular or ventricular remodeling. In some methods, the catheter is positioned within the right ventricle, wherein the myocardial wall or left ventricle may be accessed through the septal wall to position a device configured to permit reshaping of the ventricle. The device may include a line or a plurality of anchors interconnected by a line. In one arrangement, the line is a coiled member.