We report on a systematic review of the landscape of peer assessment in massive open online courses (MOOCs) with papers from 2014 to 2020 in 20 leading education technology publication venues across four databases containing education technology-related papers, addressing three research issues: the evolution of peer assessment in MOOCs during the period 2014 to 2020, the methods used in MOOCs to assess peers, and the challenges of and future directions in MOOC peer assessment. We provide summary statistics and a review of methods across the corpus and highlight three directions for improving the use of peer assessment in MOOCs: the need for focusing on scaling learning through peer evaluations, the need for scaling and optimizing team submissions in team peer assessments, and the need for embedding a social process for peer assessment.