The most well-known manifestation of the Casimir effect is the attraction of two uncharged conducting plates. However, it turns out that Casimir forces are all around us: they originate from vacuum fluctuations of the electromagnetic field that excite dipoles in dielectric and conducting materials. These dipoles then interact with each other, generating measurable forces between macroscopic bodies: the Casimir force. A naive calculation of the Casimir force produces infinities, and though extensive work has been done in the field, there is still no universal prescription to renormalize the force. In this paper, we introduce the subject of Casimir forces and focus on the Casimir self-stress inside a homogeneous sphere. We discuss previous calculations and suggest an additional renormalization scheme that could solve the problem.