Several topics which are relevant to the results and methods in this thesis are examined in Part I. Recent developments in the application of molecular orbital theory to the Diels-Alder reaction and the history and development of semi-empirical molecular orbital methods are reviewed. A survey of the major developments in understanding diastereofacial selection in the Diels-Alder reaction is also included in Part I. In Part II experimental and molecular mechanics studies are described for the addition of several azo, acetylenic and alkene dienophiles with four cage-fused dienes. Reactions of a dihydroxy substituted cage diene were found to proceed with complete selectivity for reaction from the face of the diene anti to the cyclobutane group, with the exception of the reaction of nitrosobenzene which was determined to be reversible. For most of the dienophiles, however, molecular mechanics calculations of the products in the reactions confirm that the relative stability of the adducts does not control the diastereofacial selection in the reaction. With a series of mono- and dimethylidene substituted cage-fused dienes, reactions of alkene dienophiles showed a strong preference for reaction from the anti face of the diene and this is successfully rationalized by a transition state model based on molecular mechanics. A series of mono and dimethylidene substituted cage dienes showed an opposing trend in facial selectivity, upon reaction with acetylenic dienophiles, to that observed with azo dienophiles. The selectivity observed for the reactions of acetylenic dienophiles cannot be rationalised by the "steric only" molecular mechanics based transition state models and this is interpreted as pointing to the importance of direct interactions between the substituents on the cage diene and the approaching dienophile. Several studies on the chemistry of cage-fused dienes are described with emphasis on the importance of transannular interaction during attempts to effect functional group interconversions of the cage substituents. Part III of this thesis reports studies using the AM1 and PM3 molecular orbital methods to examine several systems where orbital control may be important in determining facial selection. The reaction of acetylene with both simple dienes and cage-fused dienes is examined by application of the AM1 and PM3 methods. The reactions of acetylene with all the dienes studied are predicted to occur in reactions which are both concerted and synchronous. A detailed analysis of the energy changes in the molecular orbital energy levels during the reactions revealed destabilizing interactions involving the "orthogonal" HOMO of acetylenic dienophiles. These are important in determining the diastereofacial selection of reactions of acetylenic dienophiles with cage-fused dienes when there are suitably placed lone pairs on terminal substituents. The extent of σ/π interaction, determined by AM1 calculations for several cage-fused dienes, is shown to vary considerably with the nature of the cage substituents, but this is not considered to be an important factor in determining facial selection. As a model for substituted azo dienophiles, the Diels-Alder reactions of diimide (N₂H₂) have been studied by the PM3 method. This reaction is predicted to be both concerted and synchronous for the reaction of Z-diimide and butadiene in the exo mode but for the reaction of Z-diimide in the endo mode, the reaction is predicted to proceed via an unsymmetrical transition structure although still in a concerted reaction. The reaction of E-diimide with butadiene is considerably more complicated and three stationary points were located on the potential energy surface. The energy of aziridinium imide intermediates in possible two-step reactions of diimide and butadiene were evaluated by the PM3 method and determined to be approximately the same as the energy of the transition structures in the concerted reactions and so this precludes the involvement of these species in the reaction pathway. Finally the AM1 method was applied to examine the effect of substituents in determining the facial selection in the addition of methanol to 2,3- disubstituted-7-norbomanones and of ethylene to 5-substituted cyclopentadienes. Both of these systems have been proposed to show diastereofacial selection influenced by hyperconjugative stabilization. However, the AM1 method was not able to reproduce the observed facial selection in these reactions. The operation and function of several computer programs developed during the course work for the graphical analysis of the results of molecular mechanics and molecular orbital calculations and for quantifying σ/π interaction in dienes are described in the appendix.