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Aspect Sentiment Triplet Extraction (ASTE) has become an emerging task in sentiment analysis research, aiming to extract triplets of the aspect term, its corresponding opinion term, and its associated sentiment polarity from a given sentence. Recently, many neural networks based models with different tagging schemes have been proposed, but almost all of them have their limitations: heavily relying on 1) prior assumption that each word is only associated with a single role (e.g., aspect term, or opinion term, etc. ) and 2) word-level interactions and treating each opinion/aspect as a set of independent words. Hence, they perform poorly on the complex ASTE task, such as a word associated with multiple roles or an aspect/opinion term with multiple words. Hence, we propose a novel approach, Span TAgging and Greedy infErence (STAGE), to extract sentiment triplets in span-level, where each span may consist of multiple words and play different roles simultaneously. To this end, this paper formulates the ASTE task as a multi-class span classification problem. Specifically, STAGE generates more accurate aspect sentiment triplet extractions via exploring span-level information and constraints, which consists of two components, namely, span tagging scheme and greedy inference strategy. The former tag all possible candidate spans based on a newly-defined tagging set. The latter retrieves the aspect/opinion term with the maximum length from the candidate sentiment snippet to output sentiment triplets. Furthermore, we propose a simple but effective model based on the STAGE, which outperforms the state-of-the-arts by a large margin on four widely-used datasets. Moreover, our STAGE can be easily generalized to other pair/triplet extraction tasks, which also demonstrates the superiority of the proposed scheme STAGE.