High-Performance Computing (HPC) has become indispensable in various fields by enabling complex simulations, data analysis, and scientific research. Traditionally confined to on-premises infrastructure, the emergence of cloud computing offers new avenues for HPC, promising scalability, flexibility, and cost-effectiveness. We explore the paradigm shift towards running HPC workloads in the cloud, highlighting key benefits such as on-demand resource provisioning, elastic scaling, and access to advanced computing architectures. Additionally, we will discuss some of the current challenges, IT and engineering department are facing when running HPC on premises including resource capacity, performance optimization, and cost management, alongside strategies to mitigate these obstacles. Through a comprehensive examination of case studies and industry trends, this abstract explains the transformative potential of migrating HPC to the cloud, paving the way for enhanced computational capabilities, accelerated innovation, and broader accessibility to advanced computing resources.