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In this overview paper, data-driven learning model-based cooperative localization and location data processing are considered, in line with the emerging machine learning and big data methods. We first review (1) state-of-the-art algorithms in the context of federated learning, (2) two widely used learning models, namely the deep neural network model and the Gaussian process model, and (3) various distributed model hyper-parameter optimization schemes. Then, we demonstrate various practical use cases that are summarized from a mixture of standard, newly published, and unpublished works, which cover a broad range of location services, including collaborative static localization/fingerprinting, indoor target tracking, outdoor navigation using low-sampling GPS, and spatio-temporal wireless traffic data modeling and prediction. Experimental results show that near centralized data fitting- and prediction performance can be achieved by a set of collaborative mobile users running distributed algorithms. All the surveyed use cases fall under our newly proposed Federated Localization (FedLoc) framework, which targets on collaboratively building accurate location services without sacrificing user privacy, in particular, sensitive information related to their geographical trajectories. Future research directions are also discussed at the end of this paper.