In this paper, we introduce the first SemEval task on Multilingual and Cross-Lingual Word-in-Context disambiguation (MCL-WiC). This task allows the largely under-investigated inherent ability of systems to discriminate between word senses within and across languages to be evaluated, dropping the requirement of a fixed sense inventory. Framed as a binary classification, our task is divided into two parts. In the multilingual sub-task, participating systems are required to determine whether two target words, each occurring in a different context within the same language, express the same meaning or not. Instead, in the cross-lingual part, systems are asked to perform the task in a cross-lingual scenario, in which the two target words and their corresponding contexts are provided in two different languages. We illustrate our task, as well as the construction of our manually-created dataset including five languages, namely Arabic, Chinese, English, French and Russian, and the results of the participating systems. Datasets and results are available at: https://github.com/SapienzaNLP/mcl-wic.