Quarkonium production in high energy proton-proton and proton-nucleus collisions

We present a brief overview of the most relevant current issues related to quarkonium production in high energy proton-proton and proton-nucleus collisions along with some perspectives. After reviewing recent experimental and theoretical results on quarkonium production in pp and pA collisions, we discuss the emerging field of polarization studies. Afterwards, we report on issues related to heavy-quark production, both in pp and pA collisions, complemented by AA collisions. To put the work in broader perpectives, we emphasize the need for new observables to investigate the quarkonium production mechanisms and reiterate the qualities that make quarkonia a unique tool for many investigations in particle and nuclear physics.