This paper provides an overview of the 4-D World – Universe Model (WUM). The World – Universe Model unifies and simplifies existing Cosmological models and results into a single coherent picture, and proceeds to compare the origin, evolution, structure, ultimate fate, and parameters of the World to the Big Bang Model. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the size and age of the World; critical energy density and the gravitational parameter; temperatures of the cosmic microwave background radiation and the peak of the far-infrared radiation; observed expansion of the World and cosmological redshift; gamma-ray background and macrostructure of the World. Additionally, the Model makes predictions pertaining to masses of dark matter particles, photons, axions, and neutrinos; proposes new types of particle interactions (Super Weak and Extremely Weak) and the fundamental physical parameters of the World; explains “Pioneer Anomaly” and the rise of the solar luminosity steadily from about 70% of its current value during the last 4.6 Byr. The Model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values for calculating time dependent parameters of the World.