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Eastwood was born on 5 January 1959 in Oldham, Lancashire and educated at Sandbach School. In 1980, he graduated from St Peter's College, University of Oxford with a First Class Bachelor of Arts (BA) in Modern History, and was promoted to Master of Arts (MA) in 1985. He completed his Doctor of Philosophy (DPhil) in 1985, also from the University of Oxford.
Eastwood has held the posts of Chief Executive of the Arts and Humanities Research Board and Pro-Vice-Chancellor of Swansea University. His academic specialism is modern history, and he was fellow and senior tutor of Pembroke College, Oxford.
He was Chief Executive of the Higher Education Funding Council for England (HEFCE), a post he had held since September 2006.  Former posts also include Vice-Chancellor of the University of East Anglia and Chief Executive of the Arts and Humanities Research Board.
On 13 April 2009, he succeeded Michael Sterling as Vice-Chancellor of the University of Birmingham. In March 2011, he announced plans to raise the undergraduate tuition fees at the University of Birmingham to the maximum of £9000 (subject to OFFA approval) for courses commencing 2012/13.
He is also Chair of the QAA Steering Group for Benchmarking and a member of the QAA Board. He has contributed numerous times to several newspapers, among them The Guardian,The Sunday Telegraph and The Times. His specialist subject is 19th and 18th century British and American politics.
Eastwood was elected a Fellow of the Royal Historical Society (FRHistS) in 1991. On 25 January 2012, he was appointed a Deputy Lieutenant of the West Midlands. He was knighted in the 2014 Birthday Honours for services to higher education.
Eastwood has been criticised over large rises in his own pay in comparison to pay cuts received by less senior staff and lectures. He currently earns a basic salary of £400,000 up by 8.1% from £372,000 last year, which is seen as particularly controversial because of the 1% pay rise offered to academic and support staff. This minimal pay rise is part of an ongoing dispute by staff and their respective unions for the University to pay the living wage. 
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- "Fellows of the Royal Historical Society". Royal Historical Society. Retrieved 19 August 2012.
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- The London Gazette: . 14 June 2014.
- "Queen's birthday honours list 2014: Military". The Guardian. 13 June 2014. Retrieved 13 June 2014.
|Vice-Chancellor of the University of East Anglia
|Vice-Chancellor of the University of Birmingham