The domain of Aspect-based Sentiment Analysis, in which aspects are extracted, their sentiments are analyzed and sentiments are evolved over time, is getting much attention with increasing feedback of public and customers on social media. The immense advancements in the field urged researchers to devise new techniques and approaches, each sermonizing a different research analysis/question, that cope with upcoming issues and complex scenarios of Aspect-based Sentiment Analysis. Therefore, this survey emphasized on the issues and challenges that are related to extraction of different aspects and their relevant sentiments, relational mapping between aspects, interactions, dependencies and contextual-semantic relationships between different data objects for improved sentiment accuracy, and prediction of sentiment evolution dynamicity. A rigorous overview of the recent progress is summarized based on whether they contributed towards highlighting and mitigating the issue of Aspect Extraction, Aspect Sentiment Analysis or Sentiment Evolution. The reported performance for each scrutinized study of Aspect Extraction and Aspect Sentiment Analysis is also given, showing the quantitative evaluation of the proposed approach. Future research directions are proposed and discussed, by critically analysing the presented recent solutions, that will be helpful for researchers and beneficial for improving sentiment classification at aspect-level.