Cytology is the branch of pathology which deals with the microscopic examination of cells for diagnosis of carcinoma or inflammatory conditions. Automation in cytology started in the early 1950s with the aim to reduce manual efforts in diagnosis of cancer. The inflush of intelligent technological units with high computational power and improved specimen collection techniques helped to achieve its technological heights. In the present survey, we focus on such image processing techniques which put steps forward towards the automation of cytology. We take a short tour to 17 types of cytology and explore various segmentation and/or classification techniques which evolved during last three decades boosting the concept of automation in cytology. It is observed, that most of the works are aligned towards three types of cytology: Cervical, Breast and Lung, which are discussed elaborately in this paper. The user-end systems developed during that period are summarized to comprehend the overall growth in the respective domains. To be precise, we discuss the diversity of the state-of-the-art methodologies, their challenges to provide prolific and competent future research directions inbringing the cytology-based commercial systems into the mainstream.