Professor Wells graduated from Warwick University in 1971 and took a Masters in Law at London University in 1973. After 20 years at Cardiff University, she worked at Durham University from 2006-8, joining Bristol as Professor of Criminal Law in January 2009. Celia was awarded the OBE for services to legal education in 2006 and was President of the Society of Legal Scholars of Great Britain and Ireland in 2006-7. She was Chair of the Law sub-panel for RAE 2008 (Research Assessment Exercise) and is a member of the Bar Standards Board Education and training Committee.

Celia has actively promoted equality and diversity in legal education, founding the Women's Law Professors' Network in 1998, and in 2001 appointed PriceWaterhouseCoopersLegal Visiting Professor in Women and Law, University of Sydney. She was joint editor of the SLS flagship journal, Legal Studies 1999-2005, is a member of the Criminal Law Review Editorial Board, and General Editor Palgrave Law Texts.

Celia's research is mainly in criminal law with a particular specialism in corporate criminal liability. She is the author of Corporations and Criminal Responsibility (2nd edition OUP 2001) and of Reconstructing Criminal Law (with Nicola Lacey and Oliver Quick, 3rd edition, Cambridge University Press, 2003). Her work has been influential in the development of an organisational theory of corporate criminal liability and she provided expert advice on corporate criminal responsibility to a number of national and international bodies including: OECD Bribery Convention Working Group; the CPS in relation to the Ladbroke Grove rail crash; Specialist Adviser to the House of Commons Select Committee Inquiry into the Draft Corporate Manslaughter Bill (2005); and the International Commission of Jurists' Expert Legal Panel on Corporate Complicity in International Crimes (2006).