Gametogenesis in animal oocytes reduces the diploid genome content of germline precursors to a haploid state in gametes by discarding ¾ of the duplicated chromosomes through a sequence of two meiotic cell divisions called meiosis I and II. The assembly of the microtubule-based spindle structure that mediates this reduction in genome content remains poorly understood compared to our knowledge of mitotic spindle assembly and function. In this review, we consider the diversity of oocyte meiotic spindle assembly and structure across animal phylogeny, review recent advances in our understanding of how animal oocytes assemble spindles in the absence of the centriole-based microtubule-organizing centers that dominate mitotic spindle assembly, and discuss different models for how chromosomes are captured and moved to achieve chromosome segregation during oocyte meiotic cell division.