Illumina acquired Solexa, and shipped the first Genome Analyzer (the ancestor of the HiSeq). Clive Brown was a central figure at Solexa during their rise and acquisition, and has been at Oxford Nanopore for the last few years (he's the one who gave the talk).
There's a lot of hype in genomics, but Brown is one of the few who has delivered, which is part of the reason why MinION is getting the benefit of the doubt. Very exciting announcement.
If I remember correctly, in 2007, the Sanger method for sequencing (which involves nucleotide-by-nucleotide, laborious, gel-based sequencing) was quickly replaced by cheaper methods. We started using laser-based sequencers, along with statistics, to determine longer sequences quicker, and using computers instead of legions of grad students.
There are various versions of this graph floating around, most of which start in 2005 with the publication of the first next-generation (multiplexed) sequencing methods by pyrosequencing (454) and sequencing by ligation (George Church) for complete bacterial genomes. Costs came down very quickly after commercial release in 2006 of 454, ABI Solid (SbL), and Solexa (SbS-sequencing by synthesis). This graph in particular is referring to the cost of sequencing a human genome, which was first done on James Watson using these next generation technologies by 454 in late 2007 if I remember correctly.
http://www.genome.gov/images/content/cost_per_genome.jpg
It's surpassing Moore's law. Looks like pretty soon we'll reach the mythical $1000 mark.