The contributions given by Combinatorial Algorithms to the Life Sciences are un-controversially of strategic importance, both in terms of design principles and of habilitating technologies, e.g., BLAST is among the most referenced paper in Science and most used programs in Genomic Analysis. Yet, with the progress of ground-breaking laboratory techniques, unprecedented amounts of data need to be processed and stored, more and more outside of classic research labs. That is, the “1,000 dollars genome and 100,000 dollars analysis” scenario envisioned by E. Mardis in Genome Medicine is rapidly approaching. In this talk, we will highlight some lessons learned from the past in terms of algorithmic design for the Life Sciences and present trends in that area quite promising for the future Life Sciences. In particular, we will focus on Compressive Genomics and Algorithmic Design and Engineering for Genomic Sequence Analysis in the Cloud.