Exoskeleton robots are electrically, pneumatically, or hydraulically actuated devices that externally support the bones and cartilage of the human body while trying to mimic the human movement capabilities and augment muscle power. The lower extremity exoskeleton device may support specific human joints such as hip, knee, and ankle, or provide support to carry and balance the weight of the full upper body. Their assistive functionality for physically-abled and disabled humans is demanded in medical, industrial, military, safety applications, and other related fields. The vision of humans walking with an exoskeleton without external support is the prospect of the robotics and artificial intelligence working groups. This paper presents a survey on the design and control of lower extremity exoskeletons for bipedal walking. First, a historical view on the development of walking exoskeletons is presented and various lower body exoskeleton designs are categorized in different application areas. Then, these designs are studied from design, modeling, and control viewpoints. Finally, a discussion on future research directions is provided.