Systems Theoretic Process Analysis (STPA) is a systematic approach for hazard analysis that has been used across many industrial sectors including transportation, energy, and defense. The unstoppable trend of using Machine Learning (ML) in safety-critical systems has led to the pressing need of extending STPA to Learning-Enabled Systems (LESs). Although works have been carried out on various example LESs, without a systematic review, it is unclear how effective and generalisable the extended STPA methods are, and whether further improvements can be made. To this end, we present a systematic survey of 31 papers, summarising them from five perspectives (attributes of concern, objects under study, modifications, derivatives and processes being modelled). Furthermore, we identify room for improvement and accordingly introduce DeepSTPA, which enhances STPA from two aspects that are missing from the state-of-the-practice: (i) Control loop structures are explicitly extended to identify hazards from the data-driven development process spanning the ML lifecycle; (ii) Fine-grained functionalities are modelled at the layer-wise levels of ML models to detect root causes. We demonstrate and compare DeepSTPA and STPA through a case study on an autonomous emergency braking system.