Ultrafast ultrasonic imaging is a rapidly developing field based on the unfocused transmission of plane or diverging ultrasound waves. This recent approach to ultrasound imaging leads to a large increase in raw ultrasound data available per acquisition. Bigger synchronous ultrasound imaging datasets can be exploited in order to strongly improve the discrimination between tissue and blood motion in the field of Doppler imaging. Here we propose a spatiotemporal singular value decomposition clutter rejection of ultrasonic data acquired at ultrafast frame rate. The singular value decomposition (SVD) takes benefits of the different features of tissue and blood motion in terms of spatiotemporal coherence and strongly outperforms conventional clutter rejection filters based on high pass temporal filtering. Whereas classical clutter filters operate on the temporal dimension only, SVD clutter filtering provides up to a four-dimensional approach (3D in space and 1D in time). We demonstrate the performance of SVD clutter filtering with a flow phantom study that showed an increased performance compared to other classical filters (better contrast to noise ratio with tissue motion between 1 and 10mm/s and axial blood flow as low as 2.6 mm/s). SVD clutter filtering revealed previously undetected blood flows such as microvascular networks or blood flows corrupted by significant tissue or probe motion artifacts. We report in vivo applications including small animal fUltrasound brain imaging (blood flow detection limit of 0.5 mm/s) and several clinical imaging cases, such as neonate brain imaging, liver or kidney Doppler imaging.