The horizontally curved composite girder bridges have excellent properties, such as quick construction, good seismic performance, saving construction formwork and convenience in spatial arrangement.etc, which have greatly promoted the application of such bridges. The objective of this paper is to provide and summarize important references related to the analysis, design and construction of curved composite girder bridges. Subjects discussed in this review include (1) different curved girder bridge configurations and their applied range; (2) current specifications; (3) construction issues; (4) design methods; (5) analytical methods; (6) load distribution; (7) torsional behavior; (8) warping stresses; (9) stability; (10) ultimate load-carrying capacity; (11) dynamic and seismic response; (12) loading test; (13) long-term behavior; and (14) design details. The literature survey presented herein mainly focuses on papers written in English, Japanese and Chinese in relation to curved composite girders.