Rapid progress in digitisation and computer techniques have enabled noteworthy new pottery analysis applications in recent decades. We focus on analytical techniques directed specifically at archaeological pottery research in this survey and review the specific benefits these have brought in the field. We consider techniques based on heterogeneous sources such as drawings, photographs, 3D scans and CT volume data. The various approaches and methods are structured according to the main steps in pottery processing in archaeology: documentation, classification and retrieval. Within these categories we review the most relevant papers and identify their advantages and limitations. We evaluate both freely and commercially available analysis tools and databases. Finally, we discuss open problems and future challenges in the field of pottery analysis.