We introduce the structured scene-text spotting task, which requires a scene-text OCR system to spot text in the wild according to a query regular expression. Contrary to generic scene-text OCR, structured scene-text spotting seeks to dynamically condition both detection and recognition on user-provided regular expressions. To tackle this task, we propose the Structured TExt sPotter (STEP), a model that exploits the provided text structure to guide the OCR process. STEP is able to deal with regular expressions that contain spaces and it is not bound to detection at wordlevel granularity. Our approach enables accurate zero-shot structured text spotting in a wide variety of real-world reading scenarios and is solely trained on publicly available data. To demonstrate the effectiveness of our approach, we introduce a new challenging test dataset that contains several types of out-of-vocabulary structured text, reflecting important reading applications such as weight information, serial numbers, license plates etc. We demonstrate that STEP can provide specialized OCR performance on demand in all tested scenarios. The code and test dataset are released at https://github.com/CVC-DAG/STEP.