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Exchange bias (EB) is a unidirectional anisotropy occurring in exchange-coupled ferromagnetic/antiferromagnetic systems, such as thin films, core–shell particles, or nanostructures. In addition to a horizontal shift of the hysteresis loop, defining the exchange bias, asymmetric loops and even vertical shifts can often be found. While the effect is used in hard disk read heads and several spintronics applications, its origin is still not fully understood. Especially in nanostructures with their additional shape anisotropies, interesting and often unexpected effects can occur. Here, we provide an overview of the most recent experimental findings and theoretical models of exchange bias in nanostructures from different materials.