  In this work we provide an overview of jamming transitions in two dimensional
systems focusing on the limit of frictionless particle interactions in the
absence of thermal fluctuations. We first discuss jamming in systems with short
range repulsive interactions, where the onset of jamming occurs at a critical
packing density and where certain quantities show a divergence indicative of
critical behavior. We describe how aspects of the dynamics change as the
jamming density is approached and how these dynamics can be explored using
externally driven probes. Different particle shapes can produce jamming
densities much lower than those observed for disk-shaped particles, and we show
how jamming exhibits fragility for some shapes while for other shapes this is
absent. Next we describe the effects of long range interactions and jamming
behavior in systems such as charged colloids, vortices in type-II
superconductors, and dislocations. We consider the effect of adding obstacles
to frictionless jamming systems and discuss connections between this type of
jamming and systems that exhibit depinning transitions. Finally, we discuss
open questions such as whether the jamming transition in all these different
systems can be described by the same or a small subset of universal behaviors,
as well as future directions for studies of jamming transitions in two
dimensional systems, such as jamming in self-driven or active matter systems.
