International conventions on the carriage of goods by sea came into existence in order to ensure better allocation of risks between carriers and cargo owners. These conventions such as the Hague-Visby Rules, Hamburg Rules and the Rotterdam Rules contain rules regulating the liability of the carrier for loss of or damage to the goods, or delay in delivery. Dissatisfaction with the Hague-Visby Rules on the ground that it contained provisions which were more favourable to the carriers led to the emergence of the Hamburg Rules. However, contrary to expectations the Hamburg Rules have not gained widespread acceptance in the shipping industry. In order to achieve uniformity in the international law on the carriage of goods by sea, the Rotterdam Rules were created. In addition to its provisions on the carriage of goods by sea, the Rotterdam Rules also cover multimodal carriage. This article critically examined the carriers’ liabilities and the allocation of the burden of proof under the different regimes of the Hague-Visby rules, the Hamburg rules and the Rotterdam rules. The carrier’s duties and limits of liability were analysed with a view to highlight the differences and improvements under the regimes of the different international conventions.