This work proposes a neural network to extensively exploit spatial information for multichannel joint speech separation, denoising and dereverberation, named SpatialNet. In the short-time Fourier transform (STFT) domain, the proposed network performs end-to-end speech enhancement. It is mainly composed of interleaved narrow-band and cross-band blocks to respectively exploit narrow-band and cross-band spatial information. The narrow-band blocks process frequencies independently, and use self-attention mechanism and temporal convolutional layers to respectively perform spatial-feature-based speaker clustering and temporal smoothing/filtering. The cross-band blocks process frames independently, and use full-band linear layer and frequency convolutional layers to respectively learn the correlation between all frequencies and adjacent frequencies. Experiments are conducted on various simulated and real datasets, and the results show that 1) the proposed network achieves the state-of-the-art performance on almost all tasks; 2) the proposed network suffers little from the spectral generalization problem; and 3) the proposed network is indeed performing speaker clustering (demonstrated by attention maps).