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This article provides an overview of heavy metal contamination in rivers and assessment methods of their contamination and effects. According to literature, rivers with heavy metal contamination in surface water are mainly found in developing countries in Asia, Africa, and Latin America and the Caribbean area, while rivers with heavy metal contamination in sediments are mostly found in Europe. The increase in heavy metal contamination in rivers has led to the adoption of individual and synergistic assessment methods. Individual methods are useful in assessing the contamination and effects for a single heavy metal, while synergistic methods assess the combined contamination and effects of several heavy metals present in surface water and sediments. These two approaches have been commonly used together in recent studies to overcome the limitations of each other and provide a more comprehensive assessment. The developments, equations, advantages, limitations, and future perspectives of these methods are discussed in this review. Calculating indexes are simple, easy-to-implement, and effective methods to provide early alerts for the environmental changes and the adverse impacts on ecosystems and human health. However, calculating indexes still have limitations due to the lack of background concentrations of heavy metals in the study area. Therefore, this issue should be addressed to overcome the limitations of these methods in the future. This review provides a useful reference for future studies on heavy metal contamination in global rivers and the assessment methods for heavy metal contamination and effects.