Luminescent solar concentrators (LSCs) were developed over three decades ago as a simple route to obtain high concentration ratio for photovoltaic cells without tracking the sun. Despite their exciting theoretical potential, LSCs have thus far reached only modest concentration ratio in practice. Here, we introduce two new approaches to LSC optical design that enable significant increases in concentration ratio for any type of luminescent material. First, we discuss the conceptual basis for nonimaging optics in luminescent concentration and then present exact ray tracing results for the simplest implementation of compound parabolic concentrator-shaped edges that deliver ∼15% increase in concentration ratio with negligible decrease in optical efficiency. Second, we extend the recently introduced concept of resonance-shifting to the case of shaped substrates and demonstrate that light can be channeled through an LSC with low loss and localized at specific points, opening up entirely new directions in LSC design.