Transformers are playing an increasingly significant part in energy conversion, transmission, and distribution, which link various resources, including conventional, renewable, and sustainable energy, from generation to consumption. Power transformers and their components are vulnerable to various operational factors during their entire life cycle, which may lead to catastrophic failures, irreversible revenue losses, and power outages. Hence, it is crucial to investigate transformer condition assessment to grasp the operating state accurately to reduce the failures and operating costs and enhance the reliability performance. In this context, comprehensive data mining and analysis based on intelligent algorithms are of great significance for promoting the comprehensiveness, efficiency, and accuracy of condition assessment. In this article, in an attempt to provide and reveal the current status and evolution of intelligent algorithms for transformer condition assessment and provide a better understanding of research perspectives, a unified framework of intelligent algorithms for transformer condition assessment and a survey of new findings in this rapidly-advancing field are presented. First, the failure statistics analysis is outlined, and the developing mechanism of the transformer internal latent fault is investigated. Then, in combination with intelligent demands of the tasks in each stage of transformer condition assessment under big data, we analyze the data source in-depth and redefine the concept and architecture of transformer condition assessment. Furthermore, the typical methods widely used in transformer condition assessment are mainly divided into rule, information fusion, and artificial intelligence. The new findings for intelligent algorithms are also elaborated, including differentiated evaluation, uncertainty methods, and big data analysis. Finally, future research directions are discussed.