Glassman was first elected to the Harford County Council in 1990, representing the northern district, where he served until 1998. In 1999, he was elected to the House of Delegates, where he represented Harford until 2008. In January of that year, Glassman was appointed to the state Senate to replace J. Robert Hooper, who resigned due to health issues. Glassman won a seat in the Senate later that year. His term as a senator lasted six years, when he was first elected County Executive of Harford County in 2014. He won re-election to that post in 2018.