Smart grids are under a new kind of computational pressure. As renewable penetration, decentralization and digitalization deepen, design and scheduling problems turn combinatorial, modelling becomes multiphysics across timescales from nanoseconds to years and fault diagnostics must work from very few labelled examples. These shifts stretch the classical simulation, optimization and control workflows used at the converter and grid levels. In this Review, we ask where quantum computing could ease those bottlenecks. We treat the two levels together, because they expose the same family of difficulties and match the same family of quantum approaches - simulation, optimization, machine learning and security. Across four converter-level and five grid-level tasks, we identify where quantum approaches have a credible near-term role inside otherwise classical workflows and where they do not yet fit. We close with the shared technical and ecosystem barriers and a staged roadmap towards quantum-enabled smart grids.