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The rising popularity of explainable artificial intelligence (XAI) to understand high-performing black boxes raised the question of how to evaluate explanations of machine learning (ML) models. While interpretability and explainability are often presented as a subjectively validated binary property, we consider it a multi-faceted concept. We identify 12 conceptual properties, such as Compactness and Correctness, that should be evaluated for comprehensively assessing the quality of an explanation. Our so-called Co-12 properties serve as categorization scheme for systematically reviewing the evaluation practices of more than 300 papers published in the last 7 years at major AI and ML conferences that introduce an XAI method. We find that 1 in 3 papers evaluate exclusively with anecdotal evidence, and 1 in 5 papers evaluate with users. This survey also contributes to the call for objective, quantifiable evaluation methods by presenting an extensive overview of quantitative XAI evaluation methods. Our systematic collection of evaluation methods provides researchers and practitioners with concrete tools to thoroughly validate, benchmark and compare new and existing XAI methods. The Co-12 categorization scheme and our identified evaluation methods open up opportunities to include quantitative metrics as optimization criteria during model training in order to optimize for accuracy and interpretability simultaneously., Comment: Published in ACM Computing Surveys (DOI http://dx.doi.org/10.1145/3583558). This ArXiv version includes the supplementary material. Website with categorization of XAI methods at https://utwente-dmb.github.io/xai-papers/