ST-segment elevation myocardial infarction-cardiogenic shock (STEMI-CS) is one of the important cardiovascular diseases, with a high rate of mortality. A timely diagnosis of STEMI is important to guide treatment and reduce sudden cardiac death. Recently, machine learning (ML) methods were developed to establish predictive models to identify the in-hospital mortality risk of STEMI-CS patients. The experimental results reported in the literature showed that the ML methods obtain relatively high performance on benchmark STEMI-CS datasets. To determine how the ML methods were developed in the past years, this paper surveys recent machine learning methods developed for STEMI-CS risk prediction. The existing methods are examined through a comparison framework. After discussing the development of the field in recent years, some open problems and new emerging trends are identified.