Machine Translation (MT) is now extensively used both as a tool to overcome language barriers on the internet and as a professional tool to translate technical documentation. The technology has rapidly evolved in recent years thanks to the availability of large amounts of data in digital format and in particular parallel corpora, which are used to train Statistical Machine Translation (SMT) tools. The quality of MT has considerably improved but the translation of multiword expressions (MWEs) still represents a big and open challenge, both from a theoretical and a practical point of view (Monti, 2013). We define MWEs as any group of two or more words or terms in a language lexicon that generally conveys a single meaning, such as the Italian expressions anima gemella (soul mate), carta di credito (credit card), acqua e sapone (water and soap), piovere a catinelle (rain cats and dogs). The persistence of mistranslation of MWEs in MT outputs originates from their lexical, syntactic, semantic, pragmatic but also translational idiomaticity. Therefore, there is a need to invest in further research in order to achieve significant improvements MT and translation technologies. In particular, it is important to develop resources, mainly MWE-annotated corpora, which can be used for both MT training and evaluation purposes (Monti and Todirascu, 2016).This work focuses on the translation asymmetries between English and Italian MWEs, and how they affect the SMT performance. By translation asymmetries we mean the differences which may occur between an MWE in a source language and its equivalent in the target language, like in many-to-many word translations (En. to be in a position to → It. essere in grado di), many-to-one (En. to set free → It. liberare) and finally one-to-many correspondences (En. overcooked → It. cotto troppo). This chapter describes the evaluation of mistranslations caused by translation asymmetries concerning multiword expressions detected in the TED-MWE corpus, which contains 1,500 sentences and 31,000 EN tokens. This corpus is a subset of the TED spoken corpus (Monti et al., 2015) annotated with all the MWEs detected during the evaluation process. The corpus contains the following information: (i) the English source text, (ii) the Italian human translations (from the parallel corpus), and (iii) the Italian SMT output. All the annotators were Italian native speakers with a good knowledge of the English language and with a background in linguistics and computational linguistics. They were asked to identify all MWEs in the source text together with their translations in approximately 300 random sentences each and to evaluate the automatic translation correctness. The identified MWEs and the evaluation of both the human and the machine translation are also recorded in the corpus. This chapter will discuss (i) the related work concerning the impact of anisomorphism (the absence of an exact correspondence between words in two different languages) and the consequent translation asymmetries on MWEs translation quality in MT, (ii) the corpus, (iii) the annotation guidelines, (iv) the methodology adopted during the annotation process (Monti et al., 2015), (v) the results of the annotation and finally (vi) the evaluation of translation asymmetries in the corpus and ideas for future work.