Interstellar neutrals (ISNs), pick-up ions (PUIs), and energetic neutral atoms (ENAs) are fundamental constituents of the heliosphere and its interaction with the neighboring interstellar medium. Here, we focus on selected aspects of present-day theory and modeling of these particles. In the last decades, progress in the understanding of the role of PUIs and ENAs for the global heliosphere and its interaction with very local interstellar medium is impressive and still growing. The increasing number of measurements allows for verification and continuing development of the theories and model attempts. We present an overview of various model descriptions of the heliosphere and the processes throughout it including the kinetic, fluid, and hybrid solutions. We also discuss topics in which interplay between theory, models, and interpretation of measurements reveals the complexity of the heliosphere and its understanding. They include model-based interpretation of the ISN, PUI, and ENA measurements conducted from the Earth’s vicinity. In addition, we describe selected processes beyond the Earth’s orbit up to the heliosphere boundary regions, where PUIs significantly contribute to the complex system of the global heliosphere and its interaction with the VLISM.