The ability to model only primaries is very desirable in seismic exploration and can find broad applications in modeling, imaging, data processing, and interpretation. In this article, “primaries” mean the primary transmitted or reflected waves that involve only single interactions (transmission or reflection) at interfaces (sharp discontinuities) inside a heterogeneous medium. Primary-only modeling usually is much faster and more memory-efficient than full-wave methods, and, in addition, can provide “clean” seismograms free from multiples—a feature useful in testing certain features of migration/imaging or velocity analysis algorithms. This ability of modeling primary-only events also means the method can eliminate pure multiples from full-wave seismograms. The potential applications of primary-only modeling go beyond seismic modeling. For example, it can be applied as an extended one-way propagator to migration/imaging using unconventional waves (such as turning waves), reflected waves, or duplex waves for difficult targets.