This dissertation considers the problem of the semantic function of verbal aspectual morphology in Polish and other Slavic languages in the framework of generative syntax and semantics. Three kinds of such morphology are examined: (i) prefixes attaching directly to the root, (ii) "secondary imperfective" suffixes, and (iii) three prefixes that have a quantificational function and are able to stack on top of already prefixed verbs: "na"--"a lot," "po"--"some, a little" and the distributive "po-" . Assuming a two-tiered theory of aspect (Smith 1991), where two distinct types of grammatically encoded aspect are distinguished--Aktionsart (telicity, durativity, dynamicity) and viewpoint (PERFECTIVITY vs. IMPERFECTIVITY)--the aspectual contribution of the above listed markers is analyzed using various syntactic and semantic tests, leading to a number of new conclusions and novel accounts of various problems. It is determined that Slavic verbal prefixes are uniformly markers of telicity, and then proposed that they project as heads of the telicity-encoding projection InnerAsp. Prefixed forms are also viewpoint-PERFECTIVE (= temporally bound), but for a number of reasons this fact is attributed to a compositional restriction whereby telic predicates compose only with the PERFECTIVE viewpoint, rather than to the prefixes fulfilling that role. With regard to "secondary imperfective" suffixation, careful examination of data from Old Church Slavonic, Bulgarian and Polish reveals, contrary to what is commonly assumed, that "secondary imperfective" forms need not be interpreted IMPERFECTIVELY. Their interpretation is, on the other hand, always atelic. This leads to the novel proposal that the "secondary imperfective" morphemes correspond to a partitive-homogenizing operator, which applies to telic predicates and returns atelic ones. It is further proposed that this operator heads the InnerAsp[superscript SI] projection, merging right above InnerAsp. Lastly, with regard to quantificational prefixes, they are subjected to a two-part analysis, with the first one focusing on their unique properties, i.e., their role as intensifiers and variable quantifiers as well as their stacking ability, and the second one addressing their aspectual role. Aspectually, quantificational prefixes are shown to behave largely like other, "regular" prefixes, with only "po-" "some, a little" outside of degree achievement predicates being Aktionsart neutral. This observation puts into question a number of previous analyses which claim that such quantificational prefixes do not participate in telicity-marking. Their newly reported Aktionsart role necessitates a recursive telicity-encoding structure for all cases where a quantificational prefix attaches to a "secondary imperfective" form. This is proposed to be accomplished through an additional telicity-encoding projection InnerAsp[superscript Q], which merges with InnerAsp[superscript SI]. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]