Complex wounds usually face partial or total loss of skin thickness, healing by secondary intention. They can be acute or chronic, figuring infections, ischemia and tissue necrosis, and association with systemic diseases. Research institutes around the globe report countless cases, ending up in a severe public health problem, for they involve human resources (e.g., physicians and health care professionals) and negatively impact life quality. This paper presents a new database for automatically categorizing complex wounds with five categories, i.e., non-wound area, granulation, fibrinoid tissue, and dry necrosis, hematoma. The images comprise different scenarios with complex wounds caused by pressure, vascular ulcers, diabetes, burn, and complications after surgical interventions. The dataset, called ComplexWoundDB, is unique because it figures pixel-level classifications from $27$ images obtained in the wild, i.e., images are collected at the patients' homes, labeled by four health professionals. Further experiments with distinct machine learning techniques evidence the challenges in addressing the problem of computer-aided complex wound tissue categorization. The manuscript sheds light on future directions in the area, with a detailed comparison among other databased widely used in the literature.