Knowledge graphs effectively organize and exploit diverse real-world knowledge, alleviating limitations of purely data-driven methods and large language models, such as limited interpretability and hallucination, and serve as one of the core technologies for cognitive intelligent systems with understanding and reasoning capabilities. Knowledge graph reasoning aims to infer new knowledge from existing knowledge and is widely applied in various fields, including industrial and agricultural production, national defense and security, and daily life. Early studies on knowledge graph reasoning primarily focus on single tasks, while recent research increasingly shifts attention to more complex tasks. These complex tasks include temporal multi-step knowledge graph reasoning, few-shot multi-step knowledge graph reasoning, few-shot temporal knowledge graph reasoning, few-shot multi-modal knowledge graph reasoning, multi-modal inductive knowledge graph reasoning, and temporal inductive knowledge graph reasoning. Accordingly, this study first describes the characteristics of knowledge graph reasoning for single tasks and complex tasks. Subsequently, several representative knowledge graph reasoning techniques for single tasks are introduced. Then, existing representative knowledge graph reasoning methods for complex tasks and conduct a comparative analysis of these methods are systematically summarized and comparatively analyzed. Finally, the major remaining challenges in knowledge graph reasoning are discussed, and promising future research directions are outlined.