Finding a needle in a haystack was once a hard problem. However, magnets made finding that needle much easier. In the modern age, the vast amount of information is our haystack, and a particular piece of information is our needle, and as the title suggests, eigenvalues and eigenvectors are our magnets. In the last decades, many researchers have found more and more ways to use eigenvalues and eigenvectors as our magnets to find particular the pieces of information we are looking for. Among these include the PageRank algorithm and spectral bipartitioning. We will give the basic theory behind these techniques and explore some examples.