The incompleteness theorems are often praised as some of the most important results in logic in the 20th century. Informally, they say that for any system we have to do mathematics with, if it is strong enough to contain elementary arithmetic, then it either proves a contradiction, or fails to decide the truth of all statements. Furthermore enough arithmetic in our system guarantees that working within that system, you cannot prove its consistency. Because these theorems are important, and the way they are proved is sometimes confusing, they have been used to justify some wild claims on the nature of humanity or the universe. Therefore as mathematicians it is important to understand what these theorems say, and what they do not, and be able to explain the broad ideas to people outside of math, as well as recognize when they are being used inappropriately. I will go over what a theory is, what it means for a theory to be incomplete, discuss some examples, and then talk about the theorems and their consequences.