The Fundamental Theorem of Algebra dates back to the mid-17th century, and it can be stated quite easily: every polynomial with complex coefficients has a complex number as a root. There are numerous modern proofs of this theorem, drawing on such diverse fields as complex analysis, abstract algebra, and topology. In this talk, we will discuss at least two of these proofs, and we will touch on some of the theoretical applications. This presentation should be accessible to anyone who has completed Calculus I.