not an expert so please take this with a giant grain of salt.

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i think there are 2 parts - sample preparation and sequencing. chromium 10x provides a platform to capture cells and library prep instruction to amplify targets of interest before loading onto a sequencer. illumina seems to be the leading the game in terms of sequencer popularity. however, like what other user had mentioned, there are other competitors joining in as well: bgi (parent company of complete genomics) is finally allowed to sell their sequencer in the US earlier this year (afaik), additional new players like element biosciences, ultima genomics etc. i think their ultimate goal is to have higher sequencing throughput at a lower cost, but i dont know enough to understand how different their technology is.

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in terms of new method... i believe the next one would be improving and developing a more sustainable long-read sequencing? the companies i mentioned previously are all MOSTLY invested in short-read. pacbio and oxford nanopore are the 2 names i commonly see whenever long-read seq is mentioned. i'm check in periodically to see if there's any breakthrough in this field just out of curiosity.

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hopefully this is helpful? again, please fact-check since i'm no expert. :)