High utility itemsets mining (HUIM) is an important sub-field of frequent itemset mining (FIM). Recently, HUIM has received much attention in the field of data mining. High utility itemsets (HUIs) have proven to be quite useful in marketing, retail marketing, cross-marketing, and e-commerce. Traditional HUIM approaches suffer from a drawback as they need a user-defined minimum utility ($ min\_util $) threshold. It is not easy for the users to set the appropriate $ min\_util $ threshold to find actionable HUIs. To target this drawback, top-k HUIM has been introduced. top-k HUIM is more suitable for supermarket managers and retailers to prepare appropriate strategies to generate higher profit. In this paper, we provide an in-depth survey of the current status of top-k HUIM approaches. The paper presents the task of top-k HUIM and its relevant definitions. It reviews the top-k HUIM approaches and presents their advantages and disadvantages. The paper also discusses the important strategies of the top-k HUIM, their variations, and research opportunities. The paper provides a detailed summary, analysis, and future directions of the top-k HUIM field.