It is nearly 20 years since the landmark paper (Saitou and Nei, 1987) in MBE introducing Neighbor-Joining (NJ). This method has become the most widely-used method for building phylogenetic trees from distances, and the original paper has been cited about 13,000 times (Science Citation Index ). Yet the question ‘what does the NJ method seek to do?' has until recently proved somewhat elusive, leading to some imprecise claims and misunderstanding. However a rigorous answer to this question has recently been provided by further mathematical investigation. The origins of this story lie in a paper by Pauplin (2000) though its continuation has unfolded in more mathematically-inclined literature (Steel and Semple 2004; Desper and Gascuel, 2005). Moreover, these findings explain the superiority of recent minimum evolution-based algorithms over NJ (Desper and Gascuel, 2004; Vinh and Von Haesler, 2005). The conference will follow the same line as a recent note of Gascuel and Steel (2006), aiming to make these results more widely accessible.