We introduce Multi-SimLex, a large-scale lexical resource and evaluation benchmark covering datasets for 12 typologically diverse languages, including major languages (e.g., Mandarin Chinese, Spanish, Russian) as well as less-resourced ones (e.g., Welsh, Kiswahili). Each language dataset is annotated for the lexical relation of semantic similarity and contains 1,888 semantically aligned concept pairs, providing a representative coverage of word classes (nouns, verbs, adjectives, adverbs), frequency ranks, similarity intervals, lexical fields, and concreteness levels. Additionally, owing to the alignment of concepts across languages, we provide a suite of 66 cross-lingual semantic similarity datasets. Due to its extensive size and language coverage, Multi-SimLex provides entirely novel opportunities for experimental evaluation and analysis. On its monolingual and cross-lingual benchmarks, we evaluate and analyze a wide array of recent state-of-the-art monolingual and cross-lingual representation models, including static and contextualized word embeddings (such as fastText, M-BERT and XLM), externally informed lexical representations, as well as fully unsupervised and (weakly) supervised cross-lingual word embeddings. We also present a step-by-step dataset creation protocol for creating consistent, Multi-Simlex-style resources for additional languages. We make these contributions – the public release of Multi-SimLex datasets, their creation protocol, strong baseline results, and in-depth analyses which can be be helpful in guiding future developments in multilingual lexical semantics and representation learning – available via a website which will encourage community effort in further expansion of Multi-Simlex to many more languages. Such a large-scale semantic resource could inspire significant further advances in NLP across languages.