Challenges of connecting legacy systems with modern technologies include compatibility issues, high costs, and risk of data loss. Legacy systems often use outdated software and hardware, making integration with new applications and platforms complex. Additionally, organizations may face significant financial burdens during the transition, as updating or replacing legacy systems can be expensive. Data migration may also lead to security vulnerabilities if not managed properly. To overcome these challenges, businesses need strategic planning, adequate resources, and a clear understanding of both legacy and modern technology capabilities.