Hybrid Airships (HAs) are being touted as an efficient aerial platform for various applications involving heavy cargo transportation, communications, scientific exploration, observation, and surveillance in the stratosphere. Hybrid airship technologies have developed significantly from mid-20th century onwards, and promise to offer unique operational advantages over conventional airships. The purpose of this review paper is to explore the concepts of hybrid airship designs that have been proposed in the recent past, and highlight the current state-of-the-art in this field. Major milestones in the development of hybrid airships are presented followed by the description of types of hybrid airships and their distinct features. This review paper focuses on dynastat type of hybrid airships, since they seem to be the most promising version of hybrid airships owing to the simplicity in their designs, and suitability for various civil and military applications. The characteristics of two types of dynastat, viz., winged-hull and multiple-hull are discussed in detail. The different aspects of the conceptual design and key disciplines including aerodynamics, dynamics, performance, thermal characteristics, structure, and optimization involved in the design of hybrid airships are reviewed in detail.