The buckling analysis of an offshore pipeline refers to the analysis of temperature-induced uplift and lateral buckling of pipelines by analytical, numerical, and experimental means. Thus, the current study discusses different research performed on thermal pipe-buckling and the different factors affecting the pipeline’s buckling behaviour. The current study consists of the dependency of the pipe-buckling direction on the seabed features and burial condition; the pre-buckling and post-buckling load-displacement behaviour of the pipeline; the effect of soil weight, burial depth, axial resistance, imperfection amplitude, temperature difference, interface tensile capacity, and diameter-to-thickness ratio on the uplift and lateral resistance; and the failure mechanism of the pipeline. Moreover, the effect of external hydrostatic pressure, bending moment, initial imperfection, sectional rigidity, and diameter-to-thickness ratio of the pipeline on collapse load of the pipeline during buckling were also included in the study. This work highlights the existing knowledge on the topic along with the main findings performed up to recent research. In addition, the reference literature on the topic is given and analysed to contribute to a broad perspective on buckling analysis of offshore pipelines. This work provides a starting point to identify further innovation and development guidelines for professionals and researchers dealing with offshore pipelines, which are key infrastructures for numerous maritime applications.