DeepSeek-R1 is a cutting-edge open-source large language model (LLM) developed by DeepSeek, showcasing advanced reasoning capabilities through a hybrid architecture that integrates mixture of experts (MoE), chain of thought (CoT) reasoning, and reinforcement learning. Released under the permissive MIT license, DeepSeek-R1 offers a transparent and cost-effective alternative to proprietary models like GPT-4o and Claude-3 Opus; it excels in structured problem-solving domains such as mathematics, healthcare diagnostics, code generation, and pharmaceutical research. The model demonstrates competitive performance on benchmarks like the United States Medical Licensing Examination (USMLE) and American Invitational Mathematics Examination (AIME), with strong results in pediatric and ophthalmologic clinical decision support tasks. Its architecture enables efficient inference while preserving reasoning depth, making it suitable for deployment in resource-constrained settings. However, DeepSeek-R1 also exhibits increased vulnerability to bias, misinformation, adversarial manipulation, and safety failures - especially in multilingual and ethically sensitive contexts. This survey highlights the model's strengths, including interpretability, scalability, and adaptability, alongside its limitations in general language fluency and safety alignment. Future research priorities include improving bias mitigation, natural language comprehension, domain-specific validation, and regulatory compliance. Overall, DeepSeek-R1 represents a major advance in open, scalable AI, underscoring the need for collaborative governance to ensure responsible and equitable deployment.