Brain-inspired neuromorphic computing has been extensively researched, taking advantage of increased computer power, the acquisition of massive data, and algorithm optimization. Neuromorphic computing requires mimicking synaptic plasticity and enables near-in-sensor computing. In synaptic transistors, how to elaborate and examine the link between microstructure and characteristics is a major difficulty. Due to the absence of interlayer shielding effects, defect-free interfaces, and wide spectrum responses, reducing the thickness of organic crystals to the 2D limit has a lot of application possibilities in this computing paradigm. This paper presents an update on the progress of 2D organic crystal-based transistors for data storage and neuromorphic computing. The promises and synthesis methodologies of 2D organic crystals are summarized. Following that, applications of 2D organic crystals for ferroelectric nonvolatile memory, circuit-type optoelectronic synapses, and neuromorphic computing are addressed. Finally, new insights and challenges for the field's future prospects are presented, pushing the boundaries of neuromorphic computing even farther.