In this thesis, we extend the relational data model to incorporate partial orderings into data domains and present a comprehensive formalisation of the extended model. The main contributions of the thesis are that we show how and why such an extension can considerably improve the capabilities of capturing semantics in a wide spectrum of advanced applications such as tree-structured information, temporal information, incomplete information, fuzzy information and spatial information, whilst preserving the elegance of the theoretical basis of the model. Within the extended model, we extend the relational algebra to the Partially Ordered Relational Algebra (PORA) and the relational calculus to the Partially Ordered Relational Calculus (PORC), respectively. These two languages are shown to be equivalent. We then apply a generalized form of Paredaens' and Bancilhon's Theorem to justify our claim that the PORA is adequately expressive, i.e., non-uniformly complete. We also show that there is a one-to-one correspondence between three hierarchies of: computable queries, ordered domains and PORAs, according to the inherent structures of the underlying domains. Moreover, we formally define Ordered Functional Dependencies (OFDs) and Ordered INclusion Dependencies (OINDs) for the extended model. We then present a sound and complete axiom system for OFDs and OINDs in the case of pointwise linear orderings. In addition, we establish a set of sound and complete chase rules for OFDs in the case of lexicographical linear orderings. We extend SQL to OSQL as a query language for ordered databases. OSQL provides users with the capability to define partial orderings over data domains. In order to demonstrate the feasibility of OSQL, we have carried out an experimental implementation of the new language using the Oracle DBMS for low level data management. We have evaluated the implementation by conducting a user survey. From the results of the survey, we confirm that the essential features of OSQL which we have designed are easy to learn, understand and apply, and are useful in formulating queries involving order. Furthermore, we demonstrate that a wide range of queries in many advanced applications can be formualted in a unified manner by introducing the notion of an OSQL package.