Poor data quality is a barrier to effective, high-quality decision-making based on data. Declarative data cleaning has emerged as an effective tool for both assessing and improving the quality of data. In this work, we will address some important challenges in applying declarative data cleaning to big data, challenges that arise due to the scale, complexity, and massive heterogeneity of such data. First, we will investigate the use of domain ontologies to enhance declarative data cleaning. Second, given the dynamic nature of big data, we will develop new continuous data cleaning methods.