  In the cancer diagnosis pipeline, digital pathology plays an instrumental
role in the identification, staging, and grading of malignant areas on biopsy
tissue specimens. High resolution histology images are subject to high variance
in appearance, sourcing either from the acquisition devices or the H\&E
staining process. Nuclei segmentation is an important task, as it detects the
nuclei cells over background tissue and gives rise to the topology, size, and
count of nuclei which are determinant factors for cancer detection. Yet, it is
a fairly time consuming task for pathologists, with reportedly high
subjectivity. Computer Aided Diagnosis (CAD) tools empowered by modern
Artificial Intelligence (AI) models enable the automation of nuclei
segmentation. This can reduce the subjectivity in analysis and reading time.
This paper provides an extensive review, beginning from earlier works use
traditional image processing techniques and reaching up to modern approaches
following the Deep Learning (DL) paradigm. Our review also focuses on the weak
supervision aspect of the problem, motivated by the fact that annotated data is
scarce. At the end, the advantages of different models and types of supervision
are thoroughly discussed. Furthermore, we try to extrapolate and envision how
future research lines will potentially be, so as to minimize the need for
labeled data while maintaining high performance. Future methods should
emphasize efficient and explainable models with a transparent underlying
process so that physicians can trust their output.
