In material science and bio-medical domains the quantity and quality of microscopy images is rapidly increasing and there is a great need to automatically detect, delineate and quantify particles, grains, cells, neurons and other functional "objects" within these images. These are challenging problems for image processing because of the variability in object appearance that inevitably arises in real world image acquisition and analysis. One of the most promising (and practical) ways to address these challenges is interactive image segmentation. These algorithms are designed to incorporate input from a human operator to tailor the segmentation method to the image at hand. Interactive image segmentation is now a key tool in a wide range of applications in microscopy and elsewhere. Historically, interactive image segmentation algorithms have tailored segmentation on an image-by-image basis, and information derived from operator input is not transferred between images. But recently there has been increasing interest to use machine learning in segmentation to provide interactive tools that accumulate and learn from the operator input over longer periods of time. These new learning algorithms reduce the need for operator input over time, and can potentially provide a more dynamic balance between customization and automation for different applications. This paper reviews the state of the art in this area, provides a unified view of these algorithms, and compares the segmentation performance of various design choices.