Graphical User Interfaces (GUIs) are central to app development projects. App developers may use the GUIs of other apps as a means of requirements refinement and rapid prototyping or as a source of inspiration for designing and improving their own apps. Recent research has thus suggested retrieving relevant GUI designs that match a certain text query from screenshot datasets acquired through crowdsourced or automated exploration of GUIs. However, such text-to-GUI retrieval approaches only leverage the textual information of the GUI elements, neglecting visual information such as icons or background images. In addition, retrieved screenshots are not steered by app developers and lack app features that require particular input data. To overcome these limitations, this paper proposes GUing, a GUI search engine based on a vision-language model called GUIClip, which we trained specifically for the problem of designing app GUIs. For this, we first collected from Google Play app introduction images which display the most representative screenshots and are often captioned (i.e.~labelled) by app vendors. Then, we developed an automated pipeline to classify, crop, and extract the captions from these images. This resulted in a large dataset which we share with this paper: including 303k app screenshots, out of which 135k have captions. We used this dataset to train a novel vision-language model, which is, to the best of our knowledge, the first of its kind for GUI retrieval. We evaluated our approach on various datasets from related work and in a manual experiment. The results demonstrate that our model outperforms previous approaches in text-to-GUI retrieval achieving a Recall@10 of up to 0.69 and a HIT@10 of 0.91. We also explored the performance of GUIClip for other GUI tasks including GUI classification and sketch-to-GUI retrieval with encouraging results.