Aspect-based sentiment analysis (ABSA) aims at predicting sentiment polarity (SC) or extracting opinion span (OE) expressed towards a given aspect. Previous work in ABSA mostly relies on rather complicated aspect-specific feature induction. Recently, pretrained language models (PLMs), e.g., BERT, have been used as context modeling layers to simplify the feature induction structures and achieve state-of-the-art performance. However, such PLM-based context modeling can be not that aspect-specific. Therefore, a key question is left under-explored: how the aspect-specific context can be better modeled through PLMs? To answer the question, we attempt to enhance aspect-specific context modeling with PLM in a non-intrusive manner. We propose three aspect-specific input transformations, namely aspect companion, aspect prompt, and aspect marker. Informed by these transformations, non-intrusive aspect-specific PLMs can be achieved to promote the PLM to pay more attention to the aspect-specific context in a sentence. Additionally, we craft an adversarial benchmark for ABSA (advABSA) to see how aspect-specific modeling can impact model robustness. Extensive experimental results on standard and adversarial benchmarks for SC and OE demonstrate the effectiveness and robustness of the proposed method, yielding new state-of-the-art performance on OE and competitive performance on SC.