Handling large datasets in Power BI can lead to slow performance, memory consumption issues, and refresh failures. Power BI developers need to optimize data models by removing unnecessary columns, using aggregations, and implementing proper indexing in source databases. Partitioning data, using Power BI Premium features like large models and composite models, and leveraging Azure Synapse Analytics can help manage big data more efficiently. Using incremental refresh instead of full dataset refresh, along with optimizing relationships and avoiding excessive calculated columns, ensures better scalability and performance in Power BI.