Pretrained multilingual text encoders based on neural transformer architectures , such as multilingual BERT (mBERT) and XLM, have recently become a default paradigm for cross-lingual transfer of natural language processing models, rendering cross-lingual word embedding spaces (CLWEs) effectively obsolete. In this work we present a systematic empirical study focused on the suitability of the state-of-the-art multilingual encoders for cross-lingual document and sentence retrieval tasks across a number of diverse language pairs. We first treat these models as multilingual text encoders and benchmark their performance in unsupervised ad-hoc sentence- and document-level CLIR. In contrast to supervised language understanding, our results indicate that for unsupervised document-level CLIR-a setup with no relevance judgments for IR-specific fine-tuning-pretrained multilingual encoders on average fail to significantly outperform earlier models based on CLWEs. For sentence-level retrieval, we do obtain state-of-the-art performance: the peak scores, however, are met by multilingual encoders that have been further specialized, in a supervised fashion, for sentence understanding tasks, rather than using their vanilla 'off-the-shelf' variants. Following these results, we introduce localized relevance matching for document-level CLIR, where we independently score a query against document sections. In the second part, we evaluate multilingual encoders fine-tuned in a supervised fashion (i.e., we learn to rank ) on English relevance data in a series of zero-shot language and domain transfer CLIR experiments. Our results show that, despite the supervision, and due to the domain and language shift, supervised re-ranking rarely improves the performance of multilingual transformers as unsupervised base rankers. Finally, only with in-domain contrastive fine-tuning (i.e., same domain, only language transfer), we manage to improve the ranking quality. We uncover substantial empirical differences between cross-lingual retrieval results and results of (zero-shot) cross-lingual transfer for monolingual retrieval in target languages, which point to "monolingual overfitting" of retrieval models trained on monolingual (English) data, even if they are based on multilingual transformers.