Apart from the adverse effects on a patient’s physical and psychological well-being, wounds generally entail very high medical expenses. The inconsistent nature of clinical assessment and shortage of physicians in some regions may also impede proper wound diagnosis. Diagnosis and appropriate management of a wound depend on an understanding of its cause. The development in computer vision and medical imaging has made deep learning the most used technique to interpret wound images. In this paper, we discuss the recent advancements in deep learning applications concerning wound image analysis, particularly within wound segmentation and tissue classification. We also highlight previous work in the field, summarizing key research contributions, methodologies, and findings that have shaped the current understanding of wound image analysis. We begin by introducing the publicly available datasets and preprocessing techniques applied in the analysis of wound images. We then explore evaluation metrics used in the assessment of deep learning models. Following this, we provide an in-depth look into the implementation and result analysis of deep learning models for specific types of wounds, such as pressure ulcers, burns, and diabetic foot ulcers, including tissue classification. Finally, we conclude with a discussion of the different studies reviewed, highlighting the challenges associated with deep learning for wound image segmentation.