To facilitate effective translation modeling and translation studies, one of the crucial questions to address is how to assess translation quality. From the perspectives of accuracy, reliability, repeatability and cost, translation quality assessment (TQA) itself is a rich and challenging task. In this work, we present a high-level and concise survey of TQA methods, including both manual judgement criteria and automated evaluation metrics, which we classify into further detailed sub-categories. We hope that this work will be an asset for both translation model researchers and quality assessment researchers. In addition, we hope that it will enable practitioners to quickly develop a better understanding of the conventional TQA field, and to find corresponding closely relevant evaluation solutions for their own needs. This work may also serve inspire further development of quality assessment and evaluation methodologies for other natural language processing (NLP) tasks in addition to machine translation (MT), such as automatic text summarization (ATS), natural language understanding (NLU) and natural language generation (NLG).