Devices and systems including implants (which may be removable) and methods of using them for reducing ventricular volume. The implants described herein are cardiac implants that may be inserted into a patient's heart, particularly the left ventricle. The implant may support the heart wall, or may be secured to the heart wall. The implants are typically ventricular partitioning device for partitioning the ventricle into productive and non-productive regions in order to reduce the ventricular volume.