In recent years, researchers have focused on developing simple and efficient methods based on electrochemical biosensors to determine hydroxycinnamic acids from various real samples (wine, beer, propolis, tea, and coffee). Enzymatic biosensors represent a promising, low-cost technology for the direct monitoring of these biologically important compounds, which implies a fast response and simple sample processing procedures. The present review aims at highlighting the structural features of this class of compounds and the importance of hydroxycinnamic acids for the human body, as well as presenting a series of enzymatic biosensors commonly used to quantify these phenolic compounds. Enzyme immobilization techniques on support electrodes are very important for their stability and for obtaining adequate results. The following sections of this review will briefly describe some of the laccase (Lac) and tyrosinase (Tyr) biosensors used for determining the main hydroxycinnamic acids of interest in the food or cosmetics industry. Considering relevant studies in the field, the fact has been noticed that there is a greater number of studies on laccase-based biosensors as compared to those based on tyrosinase for the detection of hydroxycinnamic acids. Significant progress has been made in relation to using the synergy of nanomaterials and nanocomposites for more stable and efficient enzyme immobilization. These nanomaterials are mainly carbon- and/or polymer-based nanostructures and metallic nanoparticles which provide a suitable environment for maintaining the biocatalytic activity of the enzyme and for increasing the rate of electron transport.