Two-dimensional (2D) molecular materials have attracted immense attention due to their unique properties, promising a wide range of exciting applications. To understand the structure-property relationship of these low-dimensional materials, sensitive analytical tools capable of providing structural and chemical characterisation at the nanoscale are required. However, most conventional analytical techniques fail to meet this challenge, especially in a label-free and non-destructive manner under ambient conditions. In the last two decades, tip-enhanced Raman spectroscopy (TERS) has emerged as a powerful analytical technique for nanoscale chemical characterisation by combining the high spatial resolution of scanning probe microscopy and the chemical sensitivity and specificity of surface-enhanced Raman spectroscopy. In this review article, we provide an overview of the application of TERS for nanoscale chemical analysis of 2D molecular materials, including 2D polymers, biomimetic lipid membranes, biological cell membranes, and 2D reactive systems. The progress in the structural and chemical characterisation of these 2D materials is demonstrated with key examples from our as well as other laboratories. We highlight the unique information that TERS can provide as well as point out the common pitfalls in experimental work and data interpretation and the possible ways of averting them.