Health Care for Veterans. VA offers health care benefits for Veterans who may have been exposed to certain environmental hazards during military service. These services include health registry evaluations and clinical treatment at VA’s War Related Illness and Injury Study Center. Eligibility for health care benefits. Veterans first must enroll in VA’s health care system to receive care. There are many ways a Veteran may qualify. VA provides priority enrollment for health care to certain Veterans, including Veterans who have disabilities that VA has determined are military service-connected.