This dissertation investigates the processing of two types of meaning and context interactions, vagueness and imprecision, through the case study of gradable adjectives and round numerals. The first half of the dissertation, asks the question of whether vagueness and imprecision should be collapsed into one single category, or whether they should be treated as fundamentally different types of meaning and context interactions. I investigate this question through two experiments (a Visual World eye-tracking study and a judgment task study) that focus on the processing of Relative and Absolute adjectives. Existing accounts of the relative vs. absolute distinction agree in that the context-sensitivity displayed by Relative adjectives is due to vagueness. More specifically, vagueness results from the fact that these adjectives have highly flexible lexical thresholds, whose value is generally fixed by accessing contextual information. There is however less consensus about whether context-sensitive interpretations of Absolute adjectives result from threshold variability in the sense described above, or from pragmatic reasoning about imprecision. The results reported in the dissertation converge to show that participants recruit and integrate information from the visual context differently during the processing of Relative and Absolute adjectives, suggesting that the context-sensitivity of these two classes of adjectives is indeed of a different nature. I argue that these findings constitute support for theories that claim that Absolute adjectives are not lexically context-sensitive –and therefore have fixed, context-insensitive, adjectival thresholds–, and that variable interpretations of Absolute adjectives involve imprecision.,In the second half of the dissertation, I investigate the processing of imprecision in more detail. It has been claimed that comprehenders favor imprecise interpretations over precise ones whenever possible. One of the explanations that has been put forth to explain this alleged preference is that imprecise representations might be less costly to process for the comprehender. The few existing studies that have sought to empirically substantiate this claim focus on the numeral domain, and use the round vs. non-round distinction (i.e. 100 vs. 101) as a proxy for imprecise vs. precise interpretations of the numerals. The logic behind this choice is that non-round numbers usually give rise to precise interpretations, while round numbers (by assumption) tend to be interpreted imprecisely. I argue that approaching this question from this perspective introduces the confound that non-round numerals might be independently difficult to process for reasons that are orthogonal to (im)precision calculation. I suggest that the relevant comparison should therefore be between precise and imprecise interpretations of round numbers. With these goals in mind, I conducted a series of three self-paced reading studies, where I tested (im)precise interpretations of the same round numbers. Contra previous claims, the results show that imprecise interpretations are not faster to process than their precise counterparts, but rather the opposite: imprecise interpretations incur a processing penalty compared to precise interpretations, independently of whether (im)precision is signaled explicitly by means of a slack regulator (e.g. about or exactly), or through pragmatic cues (e.g. reasoning about conversational goals).