WASHINGTON, D.C. — Former Vice President Dick Cheney had a heart transplant Saturday and is recovering at a Virginia hospital, his office said.An aide to Cheney disclosed that the 71-year-old, who has had a long history of cardiovascular trouble including numerous heart attacks, had been waiting for a transplant for more than 20 months."Although the former vice president and his family do not know the identity of the donor, they will be forever grateful for this lifesaving gift," aide Kara Ahern said in a written statement that was authenticated by several of the Republican politician’s close associates.More than 3,100 Americans currently are on the national waiting list for a heart transplant. Just over 2,300 heart transplants were performed last year, according to the United Network for Organ Sharing. And 330 people died while waiting.According to UNOS, 332 people over age 65 received a heart transplant last year. The majority of transplants occur in 50- to 64-year-olds.Cheney was recovering Saturday night at the intensive care unit of Inova Fairfax Hospital in Falls Church, Va., after surgery earlier in the day.The odds of survival are good. More than 70 percent of heart transplant recipients live at least five years, although survival is a bit lower for people over age 65.The former vice president suffered a heart attack in 2010, his fifth since the age of 37.That same year, he had surgery to have a small pump installed to help his heart keep working.Called a "left ventricular assist device," or LVAD, that device took over the job of the heart’s main pumping chamber, powered by special batteries worn in a fanny pack. It helps a person live a fairly normal life while awaiting a heart transplant, although some people receive it as permanent therapy. It was one of the few steps left, short of a transplant, to stay alive in the face of what he acknowledged was "increasing congestive heart failure."In January 2011, Cheney said he was getting by on the battery-powered heart pump, which made it "awkward to walk around." He also said he hadn’t made a decision yet on a transplant, but that "the technology is getting better and better."Cheney said then that he’d "have to make a decision at some point whether I want to go for a transplant."By that point, Cheney had been dealing with cardiovascular problems for two decades.In 1988, he had had quadruple bypass surgery, and had two artery-clearing angioplasties and the operation to implant a pacemaker, a device that monitored his heartbeat.In 2005, Cheney had six hours of surgery on his legs to repair a kind of aneurysm, and in March 2007, doctors discovered deep venous thrombosis in his left lower leg. An ultrasound a month later showed the clot was getting smaller.In July 2007, he had had a minor surgical procedure to replace the pacemaker.Cheney served as former President George W. Bush’s vice president for eight years, from 2001 until 2009. Cheney was a lightning rod for criticism during Bush’s presidency, accused by opponents of often advocating a belligerent U.S. stance in world affairs during wars in Iraq and Afghanistan.Like 5 million other Americans, Cheney had congestive heart failure, meaning his heart had become too weakened to pump properly. That can happen for a variety of reasons, but Cheney’s was due to cumulative damage from five heart attacks that he had suffered since age 37.Heart failure kills 57,000 Americans a year and contributes to many more deaths.A heart transplant is a race against time. Doctors look to the waiting list for the next qualified candidate who is a good match to the newly donated heart, which typically comes from an accident victim. The patient must get to the operating room quickly, as a newly donated heart stays fresh for only about four to six hours.During a heart transplant, a mechanical pump keeps blood flowing through the body while surgeons remove the diseased heart — and in Cheney’s case, the previously implanted LVAD — and connect the new one.Patients must take immune-suppressing medication for life, to keep their body’s immune system from attacking the new, foreign organ. They typically stay in the hospital for a week or two, and require intensive cardiac rehabilitation.