Single-pixel imaging is a paradigm that enables the capture of an image from a single point detector using a spatial light modulator. This approach is particularly interesting for optical set-ups where pixelated arrays of detectors are either too expensive or too cumbersome (e.g., multispectral, infrared imaging). It acquires the inner product between the image of the scene and a set of user-defined patterns that are sequentially uploaded onto the spatial light modulator. Compressed data acquisition reduces the acquisition time, although it leads to an ill-posed reconstruction problem, which is very challenging for real-time applications. Recently, neural networks have emerged as competitive alternatives to traditional reconstruction methods. Neural networks are parametric models that are trained by exploiting large datasets. Their noniterative nature allows for fast reconstructions, which opens the door to real-time image reconstruction from compressed acquisition. In this study, we evaluate the different networks for static and dynamic imaging. In particular, we introduce a recurrent neural network that is designed to exploit the spatiotemporal redundancy in videos via a memory state. We validate our algorithms on simulated data from the UCF-101 dataset, with a resolution of 128x128 pixels and a compression ratio of 98%. We also show experimentally that we can resolve small spectral differences in the spectrum of human skin measured in vivo.