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We introduce CrossNet, a complex spectral mapping approach to speaker separation and enhancement in reverberant and noisy conditions. The proposed architecture comprises an encoder layer, a global multi-head self-attention module, a crossband module, a narrow-band module, and an output layer. Cross-Net captures global, cross-band, and narrow-band correlations in the time-frequency domain. To address performance degradation in long utterances, we introduce a random chunk positional encoding. Experimental results on multiple datasets demonstrate the effectiveness and robustness of CrossNet, achieving state-ofthe-art performance in tasks including reverberant and noisyreverberant speaker separation. Furthermore, CrossNet exhibits faster and more stable training in comparison to recent baselines. Additionally, CrossNet's high performance extends to multimicrophone conditions, demonstrating its versatility in various acoustic scenarios.