The phrase "substantial inroads" means making significant progress or achievements in a particular area or field. It implies making a significant impact or gaining considerable success in a specific endeavor. Full definition
That policy and support for research on alternative fuels will make substantial inroads in reducing transportation emissions, said Burbank. (scientificamerican.com)
Apple's iOS ecosystem has made substantial inroads in the enterprise space, and Dell isn't likely to cede its business - friendly position to Cupertino without a fight. (theverge.com)
Plus, the iPad and Android - based devices have been making substantial inroads over the past few quarters into the enterprise space, traditionally RIM's stronghold. (eweek.com)