The disposal of nuclear residue, or spent nuclear fuel, is a critical concern in the operation and long-term sustainability of nuclear power. Once fuel rods in a reactor are spent, they are highly radioactive and thermally hot, requiring immediate storage in spent fuel pools to cool down and reduce radiation. After several years, the fuel can be transferred to dry cask storage—heavily shielded steel and concrete containers that serve as a safer interim solution. However, these methods are temporary, and permanent disposal is required to ensure long-term safety. The most widely accepted solution for permanent disposal is deep geological repositories, designed to store nuclear waste in stable underground formations for thousands of years. Countries like Finland and Sweden are leading in this development, though no repository is yet operational. Efforts such as the Yucca Mountain project in the U.S. have faced political and regulatory barriers. Meanwhile, technologies such as reprocessing and MOX fuel production allow some spent fuel to be reused in reactors, reducing overall waste. Advanced reactors, like fast breeder reactors, and transmutation techniques offer future potential to minimize the longevity and volume of nuclear waste. However, these technologies are expensive, complex, and raise proliferation concerns. The safety of disposal areas is a major priority, and modern storage solutions are engineered with multi-layered protection to prevent radiation leakage. Despite rare incidents, the risk remains extremely low when best practices are followed. Public concerns persist, often stemming from mistrust or misunderstanding, which underscores the importance of transparency and regulatory oversight. The cost of nuclear waste disposal is high, but manageable through government funding and operator contributions. Compared to the environmental costs of fossil fuels, nuclear waste—although dangerous—is concentrated and easier to isolate. In the broader context of climate change and clean energy, solving the nuclear waste challenge is essential to maintaining nuclear power as a viable, low-carbon energy option for the future.