Greater awareness of environmental sustainability has driven many industries to transition from using synthetic organic solvents to greener solvents in their manufacturing. Deep eutectic solvents (DESs) have emerged as a highly promising category of green solvents with well-demonstrated and wide-ranging applications, including their use as a solvent in extraction of small-molecule bioactive compounds for food and pharmaceutical applications. The use of DES as an extraction solvent of biological macromolecules, on the other hand, has not been as extensively studied. Thereby, the feasibility of employing DES for biomacromolecule extraction has not been well elucidated. To bridge this gap, this review provides an overview of DES with an emphasis on its unique physicochemical properties that make it an attractive green solvent (e.g., non-toxicity, biodegradability, ease of preparation, renewable, tailorable properties). Recent advances in DES extraction of three classes of biomacromolecules—i.e., proteins, carbohydrates, and lipids—were discussed and future research needs were identified. The importance of DES’s properties—particularly its viscosity, polarity, molar ratio of DES components, and water addition—on the DES extraction’s performance were discussed. Not unlike the findings from DES extraction of bioactive small molecules, DES extraction of biomacromolecules was concluded to be generally superior to extraction using synthetic organic solvents.