Robert Bechtold Heilman was born in Philadelphia on July 18, 1906, to Edgar James Heilman, a Lutheran minister, and Mary Alice Bechtold Heilman. He grew up in Elizabethville and Easton, Pennsylvania, and attended Easton High School and Lafayette University. Even at an early age, Heilman was a gifted scholar, writer, and lecturer, giving both the salutatory speech at his high school commencement and the valedictory speech upon reception of his bachelor's degree in English in 1927. From 1922 to 1926 he was a student reporter for the and also wrote a regular column on student viewpoints titled "Lafayette, We Are Here." He served as a teaching fellow in 1927-1928 at Tufts University, where he met his future wife, Ruth Champlin. Heilman received his Ph.D. in English from Harvard in 1935 with his thesis .

Heilman taught at Ohio University from 1928 to 1930, and at the University of Maine from 1931 to 1935, but his first major appointment was at Louisiana State University, where he taught from 1935 to 1947. While at LSU he developed professional and personal relationships with a number of prominent southern writers and critics, many of whom were involved in the "New American Criticism" movement. He maintained these connections throughout his life. In 1948 Heilman joined the University of Washington faculty, as chair of the English department, with five other outside appointments, including the famed poet Theodore Roethke. Roethke initially distrusted Heilman, but in time they became close friends and Heilman became one of Roethke's staunchest defenders, vouching for his character and teaching on several occasions. Heilman's most notable defense of Roethke came in the form of a persuasive letter (found in box 4, folder 26) to UW Vice President Frederick Thieme at a time when state legislators were questioning the decision to give Roethke unpaid leave during his bouts of manic depression.

Under Heilman's leadership, the English department grew in national stature and many of its faculty, including Roethke, Andrew Hilen, Arnold Stein, James W. Hall, and David Wagoner, contributed prominently to the field. Heilman brought in new faculty from over 30 graduate schools and helped UW graduates find employment in at least that many other institutions. Heilman led the English department until 1971, when he turned 65, the mandatory retirement age for department chairs. He retired from teaching and became a professor emeritus at the UW in 1976 at age 70. In 1977 he spent a year as the Arnold Professor at Whitman College.

Heilman engaged in scholarly research and writing throughout his administrative career and after his retirement. He served on the editorial boards of numerous publications, including , , , , , , and . Heilman was very involved with the latter, and corresponded frequently with the journal's editor, George Core. He was also a member of the executive councils of the Modern Language Association and the American Association of University Professors. Heilman received five honorary degrees, two Guggenheim fellowships, and one fellowship from the National Endowment for the Humanities, which he used to fund three years of study and writing in London. He took sabbatical leaves in the years 1957-1958, 1964-1965, and 1971-1972.

Heilman's academic interests included 18th- and 19th-century English and American literature and William Shakespeare. He was also a lifelong sports fan and occasionally wrote about football and baseball. Heilman produced ten volumes of critical works and essays on topics including Shakespeare, dramatic forms, fiction, and the American South. He edited 12 volumes and wrote or co-wrote four textbooks on fiction and drama. Heilman sometimes wrote poetry, most notably two light-verse retirement tributes: "The Charliad," for UW president Charles E. Odegaard, and "Sol-iloquy," for UW history professor and administrator Solomon Katz.

Heilman was an active member of Phi Beta Kappa, writing reviews for from 1959 to 1990, and serving as a PBK senator (1967 to 1985) and a member of the PBK executive committee (1973 to 1982). In 1979 his book on comedy, , received the PBK Christian Gauss Award for outstanding work of criticism. Heilman made a tour of several institutions as a Phi Beta Kappa visiting scholar from 1982 to 1983.

Robert Heilman continued to write reviews and essays and to give lectures and speeches after his retirement. He also maintained active correspondence with family and colleagues. A collection of his essays titled was published by the University of Missouri Press in 1999. Robert Heilman died in 2004.