Multi-word expressions (MWEs) are fixed, conventional strings of language (e.g. idioms, collocations, binomials, proverbs) which have been found to be widespread in language use. Research has shown that MWEs exhibit an online processing advantage over control phrases by first language (L1) and second language (L2) speakers. While this line of research has helped us better understand the nature of MWEs and factors that may influence their processing in real time, there remain several gaps that future research should focus on. In this piece, we focus on four main topics related to the online processing of MWEs: (1) comprehension of MWEs by L1 and L2 speakers, (2) production of MWEs by L1 and L2 speakers, (3) the processing of modified MWEs by L1 and L2 speakers, and (4) the processing of MWEs by L1 children. Under each topic, we propose nine research tasks that will further advance our understanding of MWE processing in real time. We conclude with relevance of MWE processing research to L2 teaching and learning.