A constantly increasing number of applications from various scientific fields are finding their way towards adopting Grid technologies in order to take advantage of their capabilities: the advent of Grid environments made feasible the solution of computational intensive problems in a reliable and cost-effective way. This book chapter focuses on presenting and describing how high performance computing in general and specifically Grids can be applied in biomedicine. The latter poses a number of requirements, both computational and sharing / networking ones. In this context, we will describe in detail how Grid environments can fulfill the aforementioned requirements. Furthermore, this book chapter includes a set of cases and scenarios of biomedical applications in Grids, in order to highlight the added-value of the distributed computing in the specific domain.