This is a biographical history starting with Dr. Burnell's early life in Northern Ireland; schooling in England; growth of interests; decision to study astronomy and specialize in radio astronomy. The discussion continues with gender issues in her training, marriage and career, and the critical period during her graduate training where she worked with Tony Hewish in the construction of the 4.5 acre radio array and the work done with it takes special attention. Their discovery of pulsars is discussed in detail including her exclusion from the inner circle deliberating over the matter. Beyond her Cambridge years, the interview covers her many subsequent positions, taken in consequence of moves her husband was making in his career, the growth of public and popular recognition of her role in the discovery of pulsars. She discusses her subsequent research in gamma ray astronomy and her roles and responsibilities at Southhampton, the Mullard Space Science Centre, at Manchester and at the Open University.