In this expository talk, we begin by briefly motivating and recalling the classical notion of a spectrum, and how to obtain the stable homotopy category as it was first defined. We then examine a conceptually simpler way to view spectra – as modules over the sphere spectrum, a (noncommutative) monoid. By taking this viewpoint, we will see why defining a symmetric monoidal product on the category of spectra is problematic, just as in classical algebra, the tensor product of two \(R\)-modules does not itself necessarily carry the structure of an \(R\)-module if \(R\) is not commutative. This motivates the introduction of a symmetric group action on spectra, which turns the sphere spectrum into a commutative monoid, allowing a straightforward definition of the smash product on the category of symmetric spectra. We will conclude with a description of the stable model structure on symmetric spectra, and how it determines the classical stable homotopy category.