The jet impingement cooling technique is regarded as one of the most effective enhanced heat transfer techniques with a single-phase medium. However, in order to facilitate manufacturing, impingement with a large number of smooth circular hole jets is used in engineering. With the increasing maturity of additive technology, some new special-shaped holes (SSHs) may be used to further improve the cooling efficiency of jet impingement. Secondly, the heat transfer coefficient of the whole jet varies greatly on the impact target surface. The experiments with a large number of single smooth circular hole jets show that the heat transfer coefficient of the impact target surface will form a bell distribution—that is, the Nusselt number has a maximum value near the stagnation region, and then rapidly decreases exponentially in the radial direction away from the stagnation region. The overall surface temperature distribution is very uneven, and the target surface will form an array of cold spots, resulting in a high level of thermal stress, which will greatly weaken the structural strength and life of the equipment. Establishing how to ensure the uniformity of jet impingement cooling has become a new problem to be solved. In order to achieve uniform cooling, special-shaped holes that generate a swirling flow may be a solution. This paper presents a summary of the effects of holes with different geometrical features on the flow field and heat transfer characteristics of jet impingement cooling. In addition, the effect of jet impingement cooling with SSHs in different array methods is compared. The current challenges of jet impingement cooling technology with SSHs are discussed, as well as the prospects for possible future advances.