This dissertation develops a novel theory of the kind of agreement that has come to be known as (nominal) concord, traditionally described as obtaining between a noun and its modifiers, e.g., adjectives and determiners. The empirical focus is the concord system in Estonian, and thus a second goal of the dissertation is to describe and analyze various morphosyntactic puzzles within Estonian DPs. The core phenomena investigated are: (i) the functional structure of nominals in Estonian, including the category D and the syntax of cardinal numerals; (ii) number concord in Estonian and concord more generally; and (iii) case concord in simple DPs as well as case concord in pseudopartitives and DPs with numerals, which apparently show an alternation between case assignment and case concord. The dissertation argues for a view of morphological case wherein some cases are assigned in particular environments when no other case is available and for a view of nominal concord as an agreement phenomenon that is formally distinct from subject-verb agreement.Despite the fact that Estonian lacks definite and indefinite articles---the most common members of category D---there is evidence that Estonian nominals contain a normal amount of functional structure, including DP. I argue that we achieve a clearer understanding of the Estonian possessor system if Estonian has DP, and I show that the category D is not only for articles, but also indefinite pronouns and the wh-determiner corresponding to `which'. I then argue that cardinal numerals in Estonian can occupy either a specifier position or a position as a head in the nominal extended projection. I show how this helps explain differences in number-marking and case-marking that arise in DPs with numerals.I then turn to an analysis of nominal concord in case and number in Estonian. I argue that treating nominal concord as a DP-internal correlate of subject-verb agreement does not lead us to a better understanding of its behavior. Furthermore, I show that nominal concord exhibits some behavior that is puzzling under an Agree-based analysis: (i) adjectives show concord despite the fact that they are not in a position to c-command the source of the features, and (ii) though possessors may intervene structurally and linearly between a putative probe and goal, they do not disrupt or affect concord in any way. The novel analysis of concord that I propose does not treat it as a direct relationship between two syntactic nodes, but as the relationship between an extended projection and the elements that comprise it. The properties just listed in (i) and (ii) are exactly what we would expect under such an approach.Finally, I explore the alternation between partitive case assignment and case concord in pseudopartitives and DPs with numerals in Estonian. I show that the partitive case assignment pattern only obtains when the entire construction is in a position to receive nominative or accusative case. I argue against a so-called case-stacking analysis, wherein the alternating elements are assigned two cases in the syntax, with the outcome determined by the morphology. Because Estonian shows the alternation in both DPs with numerals and pseudopartitives, it poses interesting challenges to the existing analyses of superficially similar phenomena. I propose instead that partitive is unmarked case inside nominals, assigned only when no other case is available. The alternation between partitive assignment and case concord then becomes a matter of timing: nominative and accusative are assigned after the unmarked case assignment rule comes into effect, but the other cases are assigned early enough that there is no need to appeal to the unmarked case.