Target Speaker Extraction (TSE) is pivotal in speech communication and human-computer interaction, enabling the isolation of a specific speaker's voice from complex acoustic environments, i.e., the cocktail party scenario. Although traditional TSE systems conditioned on enrollment speech have progressed substantially, enrollment speech as a cue has inherent limitations. Its reliability degrades when the target and interfering speakers have similar voice characteristics, when intra-speaker variability (e.g. changes in emotion or speaking style) creates a mismatch between the enrollment and target speech, or when the enrollment itself is contaminated by noise or competing speakers. This review surveys deep-learning-based TSE from the perspective of auxiliary target cues drawn from multiple modalities. We organize existing methods according to five types of information used to isolate the target speaker: audio enrollment, visual, spatial, textual/semantic, and neural cues. We also trace the evolution from discriminative estimators to variational, diffusion, flow, codec, and foundation-model-based systems and summarize representative datasets and evaluation metrics. We review the benefits and limitations of different cues and discuss challenges involving synchronization, missing or unreliable observations, data scarcity, privacy, computational cost, and real-time operation. Finally, we summarize future directions concerning adaptive cue fusion, instruction-driven extraction, realistic evaluation, and trustworthy deployment. By jointly reviewing cue design, model architecture, training objectives, datasets, and evaluation metrics, this article provides an overview of the current landscape and open problems in multimodal TSE.

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