  The modern data analyst must cope with data encoded in various forms,
vectors, matrices, strings, graphs, or more. Consequently, statistical and
machine learning models tailored to different data encodings are important. We
focus on data encoded as normalized vectors, so that their "direction" is more
important than their magnitude. Specifically, we consider high-dimensional
vectors that lie either on the surface of the unit hypersphere or on the real
projective plane. For such data, we briefly review common mathematical models
prevalent in machine learning, while also outlining some technical aspects,
software, applications, and open mathematical challenges.
