Cleavage is a period after fertilization, when a 1-cell embryo starts developing into a multicellular organism. Due to a series of mitotic divisions, the large volume of a fertilized egg is divided into numerous smaller, nucleated cells-blastomeres. Embryos of different phyla divide according to different patterns, but molecular mechanism of these early divisions remains surprisingly conserved. In the present paper, we describe how polarity cues, cytoskeleton and cell-to-cell communication interact with each other to regulate orientation of the early embryonic division planes in model animals such as Caenorhabditis elegans, Drosophila and mouse. We focus particularly on the Par pathway and the actin-driven cytoplasmic flows that accompany it. We also describe a unique interplay between Par proteins and the Hippo pathway in cleavage mammalian embryos. Moreover, we discuss the potential meaning of polarity, cytoplasmic dynamics and cell-to-cell communication as quality biomarkers of human embryos.