In contemporary society, industrialization and rising of terrorism threats highlight the necessity and importance of structural protection against accidental and intentionally malicious blast loads. Consequences of these extreme loading events are known to be catastrophic, involving personnel injuries and fatalities, economic loss and immeasurable social disruption. These impacts are generated not only from direct explosion effects, that is, blast overpressure and primary or secondary fragments, but also from the indirect effects such as structural collapse. The latter one is known to be more critical leading to massive losses. It is therefore imperative to enlighten our structural engineers and policy regulators when designing modern structures. Towards a better protection of concrete structures, efforts have been devoted to understanding properties of construction materials and responses of structures subjected to blast loads. Reliable blast resistance design requires a comprehensive knowledge of blast loading characteristics, dynamic material properties and dynamic response predictions of structures. This article presents a state-of-the-art review of the current blast-resistant design and analysis of concrete structures subjected to blast loads. The blast load estimation, design considerations and approaches, dynamic material properties at high strain rate, testing methods and numerical simulation tools and methods are considered and reviewed. Discussions on the accuracies and advantages of these current approaches and suggestions on possible improvements are also made.