What is the state of automated quantitative analysis?
The word to look for is 'Image segmentation'. But also here, it very much depends on what you're looking at. Segmentation and quantification of simple fluorescence images is relatively easy and widely used. It can get very complex depending on how complex the structure is you're looking at. There are machine-learning approaches which are able to distinguish complicated structures from each other, such as different mitosis states. 

Segmenting Hematoxylin-Eosin (HE) stained specimens is subject of intensive bioinformatical research. One goal is to assist pathologists in grading tissue lesions, such as in prostate cancer, but this is as far as I know not used clinically yet. Whole-slide scans of histological specimens are becoming more widely used clinically. These images are very huge (1 GB per specimen), so a research focus is also to provide a large-scale analysis of these whole-slide scans.

Also, take a look at CellProfiler (http://www.cellprofiler.org), this free open-source software saved my PhD project.

Literature I found:

Tabesh, A., M. Teverovskiy, et al. (2007). "Multifeature prostate cancer diagnosis and Gleason grading of histological images." IEEE Trans Med Imaging 26(10): 1366-1378.

Petushi, S., F. U. Garcia, et al. (2006). "Large-scale computations on histology images reveal grade-differentiating parameters for breast cancer." BMC Med Imaging 6: 14. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1634843/

I cannot provide you with a recent review, though...