In this demonstration we showcase REmatch, a regular expression (RegEx) engine built to find all matches of a given pattern in a document. REmatch is based on the theory of enumeration algorithms, and it extends the capability of classical regex engines with the ability to find nested and overlapping matches with a simple and intuitive syntax, and no need to use non-standard operators, while at the same time maintaining efficient performance. The algorithmic core of REmatch is an algorithm that builds a compressed representation of all matching results and enumerates them on demand in time proportional to writing them down symbol by symbol. For this demonstration, we developed a simple Web interface to access the REmatch engine, available at https://rematch.cl, and will showcase the utility of the engine in the context of analysing DNA sequences, linguistic analysis, among others. For this, we have prepared a series of examples that illustrate the expressiveness and ease of use of REmatch. Additionally, at the demo we will have a series of challenge tasks, asking attendees to capture the result set of a simple REmatch expression using their favourite RegEx engine.