Aptamers are nucleic acids referred to as chemical antibodies as they bind to their specific targets with high affinity and selectivity. They are selected via an iterative process known as ‘selective evolution of ligands by exponential enrichment’ (SELEX). Aptamers have been developed against numerous cancer targets and among them, many tumor cell-membrane protein biomarkers. The identification of aptamers targeting cell-surface proteins has mainly been performed by two different strategies: protein- and cell-based SELEX, when the targets used for selection were proteins and cells, respectively. This review aims to update the literature on aptamers targeting tumor cell surface protein biomarkers, highlighting potentials, pitfalls of protein- and cell-based selection processes and applications of such selected molecules. Aptamers as promising agents for diagnosis and therapeutic approaches in oncology are documented, as well as aptamers in clinical development.