Approximately 2 billion years ago, during the Proterozoic eon, life on Earth underwent a rapid increase in cellular complexity. The eukaryotic cell, from which we are all descended, emerged as the product of the union of the existing domains of life at the time: the archaea and the bacteria. Recent models propose that eukaryotes emerged from the fusion of an Asgard archaea and an Alphaproteobacterium. However, due Asgard archaeal phyla largely remaining uncultivated, determining which characteristics eukaryotes inherited from their archaeal ancestors remains elusive. In studying the evolutionarily and ecologically significant microbial mats of Shark Bay, Western Australia, we have found Asgard archaea to be the most dominant archaeal group in the communities. From these microbial mats, we have enriched for four phyla of Asgard archaea, including Lokiarchaeota, Heimdallarchaeota, Odinarchaeota, and Thorarchaeota. These Asgard archaea display a range of complex morphologies, ranging from small coccoid cells to long filaments. These archaea also displayed the capacity to form strange cell-body protrusions. Characterisation of the structural biology of Asgard archaea through cryogenic transmission electron microscopy and fluorescent microscopy has revealed these cells are in possession of cellular characteristics reminiscent of the eukaryotic cell. The presence of eukaryotic-like characteristics in Asgard archaeal lineages provides strong evidence for the evolution of the eukaryotic cell from relatives of the Asgard archaea, addressing the dichotomy of prokaryotic and eukaryotic cells.