||Theoretical studies on the reaction mechanisms of copper(I) catalyzed borylation of unsaturated compounds such as olefins, aldehydes and α,β-unsaturated carbonyls with diboron reagents as well as carboxylation of arylboronate esters with CO2 are reported in this thesis. The insertion reactions of alkenes into the Cu-B bond in (NHC)Cu(boryl) complexes (NHC = N-heterocyclic carbene) were studied via DFT calculations. The nature of the insertion reactions and the relevant regiochemistry were examined along with β-hydride eliminations followed by reinsertion of the alkene into the Cu-H bond. The relative reactivity of B2cat2 versus B2pin2 in the diboration reaction of alkenes catalyzed by carbene-ligated copper(I) complexes was studied using DFT calculations. Transmetallation reactions of B2cat2 and B2pin2 with (NHC)Cu-OMe were investigated. The detailed mechanism for the diboration of aldehydes catalyzed by (NHC)Cu(boryl) complexes was studied with the aid of DFT calculations. Aldehyde firstly inserted into Cu-B through a nucleophilic attack to give a Cu-O-C(boryl) species followed by σ-bond metathesis with a diboron reagent. We also studied the catalyzed diboration of 2-pyridinecarboxaldehyde, which gave the unexpected reductive coupling product 1,2-di-2-pyridyl-1,2-bis(pinacolboroxy)ethane. The detailed mechanism of the borylation of acrolein and methylacrylate catalyzed by phosphine copper(I) boryl complexes were theoretically investigated. The results showed that the catalyzed borylation occured through C=C insertion into Cu-B to give a β-borylalkyl C-bound Cu(I) enolate intermediate. In the borylation of acrolein, the C-bound Cu(I) enolate underwent a keto-to-enol isomerization to give an O-bound enolate intermediate followed by a σ-bond metathesis with a diboron reagent. While in the borylation of methylacrylate, a keto-to-enol isomerization did not occur due to the inertness of the ester group, but the addition of methanol enhanced the efficiency of the β-borylation. The insertion reactions of ethene, formaldehyde, acrolein and methylacrylate into a Cu-B bond were compared. In addition, the thermodynamics and kinetics of interconversions between O- and C-bound enolates of Cu, B, and Si were investigated. Carboxylation reactions of arylboronate esters with CO2 catalyzed by (NHC)Cu(OMe) was studied by DFT calculations. Transmetalation proceeded via a B-O-Cu bridged intermediate, which was formed from the KOR adduct of the arylboronic acid, or by CuOR complex, was studied. Insertion of CO2 into the Cu-Ar bond was found to be the rate-determining step, in which nucleophilic attack of the aryl ligand on the electron deficient carbon atom of CO2 led to the formation of a new C-C bond. Alkylboronic esters, but not alkynylboronic esters, were predicted to be suitable substrates for the reaction.