Wound healing is a physiological process occurring after the onset of a skin lesion aiming to reconstruct the dermal barrier between the external environment and the body. Depending on the nature and duration of the healing process, wounds are classified as acute (e.g., trauma, surgical wounds) and chronic (e.g., diabetic ulcers) wounds. The latter take several months to heal or do not heal (non-healing chronic wounds), are usually prone to microbial infection and represent an important source of morbidity since they affect millions of people worldwide. Typical wound treatments comprise surgical (e.g., debridement, skin grafts/flaps) and non-surgical (e.g., topical formulations, wound dressings) methods. Modern experimental approaches include among others three dimensional (3D)-(bio)printed wound dressings. The present paper reviews recently developed 3D (bio)printed hydrogels for wound healing applications, especially focusing on the results of their in vitro and in vivo assessment. The advanced hydrogel constructs were printed using different types of bioinks (e.g., natural and/or synthetic polymers and their mixtures with biological materials) and printing methods (e.g., extrusion, digital light processing, coaxial microfluidic bioprinting, etc.) and incorporated various bioactive agents (e.g., growth factors, antibiotics, antibacterial agents, nanoparticles, etc.) and/or cells (e.g., dermal fibroblasts, keratinocytes, mesenchymal stem cells, endothelial cells, etc.).