Volinsky was born in New York City and grew up in Levittown, Pennsylvania, graduating from Woodrow Wilson High School in 1973.

Volinsky earned a Bachelor of Arts degree in psychology from the University of Miami, which he attended on scholarship, graduating magna cum laude in 1976.

[citation needed] During law school, Volinsky met his wife, Amy Goldstein, who is a fellow attorney and public service advocate.

The fundamental rights established in the Claremont cases have never been completely implemented, resulting in the NH Court deciding again in 2019 that the state failed to meet its constitutional obligation.

The Eversource project sought to build nearly 200 miles of high-voltage transmission lines through New Hampshire, to connect large-scale hydropower from Quebec to Massachusetts.

The Site Evaluation Committee denied the necessary permits for the project and Andru’s work at the Supreme Court helped sustain that denial.

The work of Volinsky's legal team resulted in the return of more than $50 million in overpaid premiums from the Local Government Center Risk Pools to New Hampshire municipalities and school districts.

[13] In 2014, Volinsky represented four large public unions who sought to challenge the State's effort to shift increased pension costs to existing employees.

[18] In the 2024 Democratic primary, Volinsky urged voters to write-in "ceasefire" in protest of President Joe Biden's approach to the Israel–Hamas war.