Abstract Cross-lingual word embeddings (CLEs) facilitate cross-lingual transfer of NLP models. Despite their ubiquitous downstream usage, increasingly popular projection-based CLE models are almost exclusively evaluated on bilingual lexicon induction (BLI). Even the BLI evaluations vary greatly, hindering our ability to correctly interpret performance and properties of different CLE models. In this work, we take the first step towards a comprehensive evaluation of CLE models: we thoroughly evaluate both supervised and unsupervised CLE models, for a large number of language pairs, on BLI and three downstream tasks, providing new insights concerning the ability of cuttingedge CLE models to support cross-lingual NLP. We empirically demonstrate that the performance of CLE models largely depends on the task at hand and that optimizing CLE models for BLI may hurt downstream performance. We indicate the most robust supervised and unsupervised CLE models and emphasize the need to reassess simple baselines, which still display competitive performance across the board. We hope our work catalyzes further research on CLE evaluation and model analysis.