Over the past few years, technological advances have allowed for measurement of omics data at the cell level, creating a new type of data generally referred to as single-cell (sc) omics. On the other hand, the so-called spatial omics are a family of techniques that generate biological information in a spatial domain, for instance, in the volume of a tissue. In this survey, we are mostly interested in the intersection between sc and spatial (scs) omics and in the challenges and opportunities that this new type of data pose for downstream data analysis methodologies. Our goal is to cover all major omics modalities, including transcriptomics, genomics, epigenomics, proteomics and metabolomics.