"Problems and Theorems in Sequence Comparison" Christian Houdré, Georgia Tech Some questions, stemming from the longest common subsequence (LCS) paradigm, will be adressed. Starting with one sequence and the longest increasing subsequence (LIS) problem, for finite alphabets, new classes of Brownian functionals will be obtained as limiting laws. If time permits, further results on the order of the variance of the length of the LCS will be presented.