Developing Quantitative Structure-Activity Relationship (QSAR) models applicable to general molecules is of great significance for molecular design in many disciplines. This paper reviews the development and current status of molecular QSAR research, including datasets, molecular descriptors, and mathematical models. A representative bibliometric analysis reveals the evolutionary trends in this field in the past decade. Based on the discussion of the advantages and shortcomings of existing methods, the requirements and possible approaches for developing a widely applicable QSAR model were put forward. This goal poses a series of challenges to QSAR, including: (1) Having a sufficient number of structure-activity relationship instances as training data to cope with the complexity and diversity of molecular structures and action mechanisms; (2) Developing and using precise molecular descriptors to avoid the situation of ‘garbage in, garbage out’, while balancing descriptor dimensions and computational costs; and (3) Using powerful and flexible mathematical models, such as deep learning models, to learn complex functional relationships between descriptors and activity. With the emergence of larger and higher-quality data sets, more accurate molecular descriptors and deep learning methods, predictive ability, interpretability and application domain of QSAR models will continue to improve, and it will play a more important role in various fields of molecular design.