Behavioural research over several decades has found that concrete words are processed more quickly and accurately than abstract words (concreteness effect). This advantage is also reflected in their different processing and representation in the human brain. In this electrophysiological study, we explored the interplay of concreteness as a continuous measure and task effects on word processing. Electrophysiological responses of 58 participants were recorded during semantic, affective, and grammatical decision tasks on words parametrically varied in concreteness. Our findings uncovered a fine-grained concreteness effect within four distinct spatiotemporal windows when a coding of semantic information is required. In the semantic decision task, we detected a higher parietal positivity within the P300 time range and an increased left temporo-lateral negative-going amplitude for less concrete concepts. We also identified a concreteness effect characterised by greater negativity in the N400 component. In the affective task, we observed a more pronounced parietal P600-like component for more abstract concepts. Interestingly, we found that the neural representational similarity (starting from 450 ms with a widespread scalp distribution) conformed to the concreteness similarity among concepts (regardless of the task), implying that their semantic representations may be characterised along the concreteness dimension in the brain. Our study transcends the conventional dichotomy of abstract versus concrete words, unearthing not only varied processing dynamics along the concreteness dimension but also distinct fine-grained neural representations. This novel insight positions concreteness as a structural dimension, enriching our comprehension of how the brain organises and processes semantic information.