Facetto is a scalable visual analytics application that is used to discover single-cell phenotypes in high-dimensional multi-channel microscopy images of human tumors and tissues. Such images represent the cutting edge of digital histology and promise to revolutionize how diseases such as cancer are studied, diagnosed, and treated. Highly multiplexed tissue images are complex, comprising 10^9 or more pixels, 60-plus channels, and millions of individual cells. This makes manual analysis challenging and error-prone. Existing automated approaches are also inadequate, in large part, because they are unable to effectively exploit the deep knowledge of human tissue biology available to anatomic pathologists. To overcome these challenges, Facetto enables a semi-automated analysis of cell types and states. It integrates unsupervised and supervised learning into the image and feature exploration process and offers tools for analytical provenance. Experts can cluster the data to discover new types of cancer and immune cells and use clustering results to train a convolutional neural network that classifies new cells accordingly. Likewise, the output of classifiers can be clustered to discover aggregate patterns and phenotype subsets. We also introduce a new hierarchical approach to keep track of analysis steps and data subsets created by users; this assists in the identification of cell types. Users can build phenotype trees and interact with the resulting hierarchical structures of both high-dimensional feature and image spaces. We report on use-cases in which domain scientists explore various large-scale fluorescence imaging datasets. We demonstrate how Facetto assists users in steering the clustering and classification process, inspecting analysis results, and gaining new scientific insights into cancer biology.