This book constitutes the refereed joint proceedings of the Second International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2018 and the First International Workshop on Integrating Medical Imaging and Non-Imaging Modalities, Beyond MIC 2018, held in conjunction with the 21st International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2018, in Granada, Spain, in September 2018. The 6 full papers presented at GRAIL 2018 and the 5 full papers presented at BeYond MIC 2018 were carefully reviewed and selected. The GRAIL papers cover a wide range of develop graph-based models for the analysis of biomedical images and encourage the exploration of graph-based models for difficult clinical problems within a variety of biomedical imaging contexts. The Beyond MIC papers cover topics of novel methods with significant imaging and non-imaging components, addressing practical applications and new datasets