Abstract: (Coffee @ 3:00) Legendre pairs were introduced in 2001 by Seberry and her students, as a means to construct Hadamard matrices via a two-circulant core construction. Legendre pairs of every odd prime length exist, via a simple construction using the Legendre symbol. We will review known constructions for Legendre pairs. We will discuss various results on Legendre pairs during the past 20+ years, including the concept of compression, introduced in a joint paper with D. Z. Djokovic, as well as the computational state-of-the-art of the search for Legendre pairs. Finally, we will discuss a Coding Theory reformulation of the problem of enumerating Legendre pairs for a given odd length ell, via computing the weight enumerator of a binary code, based on work of S. Eliahou. The importance of Legendre pairs lies in the fact that they constitute a promising avenue to the Hadamard conjecture.