AbstractState-of-the-art neural (re)rankers are notoriously data-hungry which – given the lack of large-scale training data in languages other than English – makes them rarely used in multilingual and cross-lingual retrieval settings. Current approaches therefore commonly transfer rankers trained on English data to other languages and cross-lingual setups by means of multilingual encoders: they fine-tune all parameters of pretrained massively multilingual Transformers (MMTs, e.g., multilingual BERT) on English relevance judgments, and then deploy them in the target language(s). In this work, we show that two parameter-efficient approaches to cross-lingual transfer, namely Sparse Fine-Tuning Masks (SFTMs) and Adapters, allow for a more lightweight and more effective zero-shot transfer to multilingual and cross-lingual retrieval tasks. We first train language adapters (or SFTMs) via Masked Language Modelling and then train retrieval (i.e., reranking) adapters (SFTMs) on top, while keeping all other parameters fixed. At inference, this modular design allows us to compose the ranker by applying the (re)ranking adapter (or SFTM) trained with source language data together with the language adapter (or SFTM) of a target language. We carry out a large scale evaluation on the CLEF-2003 and HC4 benchmarks and additionally, as another contribution, extend the former with queries in three new languages: Kyrgyz, Uyghur and Turkish. The proposed parameter-efficient methods outperform standard zero-shot transfer with full MMT fine-tuning, while being more modular and reducing training times. The gains are particularly pronounced for low-resource languages, where our approaches also substantially outperform the competitive machine translation-based rankers.