Three-dimensional (3D) printing technology has opened a new paradigm to controllably and reproducibly fabricate bioengineered neural constructs for potential applications in repairing injured nervous tissues or producing in vitro nervous tissue models. However, the complexity of nervous tissues poses great challenges to 3D-printed bioengineered analogues, which should possess diverse architectural/chemical/electrical functionalities to resemble the native growth microenvironments for functional neural regeneration. In this work, we provide a state-of-the-art review of the latest development of 3D printing for bioengineered neural constructs. Various 3D printing techniques for neural tissue-engineered scaffolds or living cell-laden constructs are summarized and compared in terms of their unique advantages. We highlight the advanced strategies by integrating topographical, biochemical and electroactive cues inside 3D-printed neural constructs to replicate in vivo-like microenvironment for functional neural regeneration. The typical applications of 3D-printed bioengineered constructs for in vivo repair of injured nervous tissues, bio-electronics interfacing with native nervous system, neural-on-chips as well as brain-like tissue models are demonstrated. The challenges and future outlook associated with 3D printing for functional neural constructs in various categories are discussed.