The jet in crossflow, or transverse jet, is a flowfield that has relevance to a wide range of energy and propulsion systems. Over the years, our group's studies on this canonical flowfield have focused on the dynamics of the vorticity associated with equidensity and variable density jets in crossflow, including the stability characteristics of the jet's upstream shear layer, as a means of explaining jet response to altered types of excitation. The jet's upstream shear layer is demonstrated to exhibit convectively unstable behavior at high jet-to-crossflow momentum flux ratios, transitioning to absolutely unstable behavior at low momentum flux and/or density ratios, with attendant differences in shear layer vorticity evolution and rollup. These differences in stability characteristics are shown to have a significant effect on how one optimally employs external excitation to control jet penetration and spread, depending on the flow regime and specific engineering application. Yet recent unexpected observations on altered transverse jet structure under different flow conditions introduce a host of unanswered questions, primarily but not exclusively associated with the nature of molecular mixing, that make this canonical flowfield one that is of great interest for more extensive exploration.