High Utility Itemset (HUI) mining problem is one of the important problems in the data mining literature. The problem offers greater flexibility to a decision maker to incorporate her/his notion of utility into the pattern mining process. The problem, however, requires the decision maker to choose a minimum utility threshold value for discovering interesting patterns. This is quite challenging due to the disparate itemset characteristics and their utility distributions. In order to address this issue, Top-K High Utility Itemset (THUI) mining problem was introduced in the literature. THUI mining problem is primarily a variant of the HUI mining problem that allows a decision maker to specify the desired number of HUIs rather than the minimum utility threshold value. Several algorithms have been introduced in the literature to efficiently mine top-k HUIs. This paper systematically analyses the top-k HUI mining methods in the literature, describes the methods, and performs a comparative analysis. The data structures, threshold raising strategies, and pruning strategies adopted for efficient top-k HUI mining are also presented and analysed. Furthermore, the paper reviews several extensions of the top-k HUI mining problem such as data stream mining, sequential pattern mining and on-shelf utility mining. The paper is likely to be useful for researchers to examine the key methods in top-k HUI mining, evaluate the gaps in literature, explore new research opportunities and enhance the state-of-the-art in high utility pattern mining.