While the upcoming telescopes will reveal correspondingly fainter, more distant galaxies, a question will persist: what more is there that these telescopes cannot see? One answer is the source-subtracted Cosmic Infrared Background (CIB). The CIB is comprised of the collective light from all sources remaining after known, resolved sources are accounted for. Ever-more-sensitive surveys will identify the brightest of these, allowing them to be removed, and - like peeling layers off an onion - reveal deeper layers of the CIB. In this way it is possible to measure the contributions from populations not accessible to direct telescopic observation. Measurement of fluctuations in the source-subtracted CIB, i.e., the spatial power spectrum of the CIB after subtracting resolved sources, provides a robust means of characterizing its faint, and potentially new, populations. Studies over the past 15 years have revealed source-subtracted CIB fluctuations on scales out to ~100 which cannot be explained by extrapolating from known galaxy populations. Moreover, they appear highly coherent with the unresolved Cosmic X-ray Background, hinting at a significant population of accreting black holes among the CIB sources. Characterizing the source-subtracted CIB with high accuracy, and thereby constraining the nature of the new populations, is feasible with upcoming instruments and would produce critically important cosmological information in the next decade. New coextensive deep and wide-area near-infrared, X-ray, and microwave surveys will bring decisive opportunities to examine, with high fidelity, the spatial spectrum and origin of the CIB fluctuations and their cross-correlations with cosmic microwave and X-ray backgrounds, and determine the formation epochs and the nature of the new sources (stellar nucleosynthetic or accreting black holes).