The by far dominating DNA sequencing company of the late 2000's and 2010's due to having the smallest cost per base pair.
Illumina actually bought their 2010's dominating technology from a Cambridge company called Solexa.
To understand how Illumina's technology works basically, watch this video: Video 1. "Illumina Sequencing by Synthesis by Illumina (2016)".
Video 1. Illumina Sequencing by Synthesis by Illumina (2016) Source.
The key innovation of this method is the Bridge amplification step, which produces a large amount of identical DNA strands.
This is one of the the key innovations of the Illumina (originally Solexa) sequencing.
This step is genius because sequencing is basically a signal-to-noise problem, as you are trying to observe individual tiny nucleotides mixed with billions of other tiny nucleotides.
With bridge amplification, we group some of the nucleotides together, and multiply the signal millions of times for that part of the DNA.
Figure 1. Illustration of the bridge amplification step of Illumina sequencing. Source.
This is one of the prime examples of Europe's decline.
Instead of trying to dominate the sequencing market and gain trillions of dollars from it, they local British early stage investors were more than happy to get a 20x return on their small initial investments, and sold out to the Americans who will then make the real profit.
And now Solexa doesn't even have its own Wikipedia page, while Illumina is set out to be the next Microsoft. What a disgrace.
Here are some good articles about the company:
Cambridge visitors can still visit the Panton Arms pub, which was the location of the legendary "hey we should talk" founders meeting, chosen due to its proximity to the chemistry department of the University of Cambridge.
In 2021 the founders were awarded the Breakthrough Prize. The third person awarded was Pascal Mayer. He was apparently at Serono Pharmaceutical Research Institute at the time of development. They do have a wiki page unlike Solexa: They paid a 700 million fine in 2005 in the United States, and sold out in 2006 to Merck for 10 billion USD.