Mucin 1 protein (MUC1) is a membrane-associated glycoprotein overexpressed in the majority of human malignancies and considered as a predominant protein biomarker in cancers. Owing to the crucial role of MUC1 in cancer dissemination and metastasis, detection and quantification of this biomarker is of great importance in clinical diagnostics. Today, there exist a wide variety of strategies for the determination of various types of disease biomarkers, especially MUC1. In this regard, aptamers, as artificial single-stranded DNA or RNA oligonucleotides with catalytic and receptor properties, have drawn lots of attention for the development of biosensing platforms. So far, various sensitivity-enhancement techniques in combination with a broad range of smart nanomaterials have integrated into the design of novel aptamer-based biosensors (aptasensors) to improve detection limit and sensitivity of analyte determination. This review article provides a brief classification and description of the research progresses of aptamer-based biosensors and nanobiosensors for the detection and quantitative determination of MUC1 based on optical and electrochemical platforms.