In this study, the reactions of C5H9 radicals are theoretically investigated, with a particular emphasis on hydrogen atom addition reactions to 1,3-pentadiene (C5H8) to form C5H9 radicals, although the subsequent isomerization and decomposition reactions of the C5H9 radicals are also of direct relevance to the radicals formed from the pyrolysis and oxidation of species including pentene and cyclopentane. MOreover, H-atom abstraction reactions by hydrogen atoms from 1,3-pentadiene are also investigated. The geometries and frequencies of 63 potential energy surface (PES) minima and 88 transition states are optimized at the omega B97XD/aug-cc-pVTZ level of theory. Spin-unrestricted open- shell single-point energies for all the species are calculated at the CCSD(T)/aug-cc-pVTZ level of theory with basis set corrections from MP2/aug-cc-pVXZ (where X = T and Q). A one-dimensional hindered rotor treatment is employed for torsional modes, with the M06-2X/6-311++G(D,P) method used to compute the potential energy as a function of the dihedral angle. The high-pressure limiting rate constants and the thermochemical properties for C-5 species are calculated using the Master Equation System Solver (MESS) with conventional transition-state theory and comparisons made with existing available literature data. A hydrogen atom can add to the terminal carbon atom of 1,3-pentadiene to form the 2,4-C5H9 radical and/or the internal carbon atoms to form 2,S-C5H9, 1,4-C5H9, and 1,3-C5H9 radicals. Among the four entrance channels for ft atom addition reactions, the formation of 2,4-C5H9 and 1,3-C5H9 radicals is more exothermic in comparison to the other C5H9 isomers (2,5-C5H9, 1,4-C5H9) because of the resonantly stabilized allylic structure. Consequently, the formation of the former is generally dominant in terms of barrier heights. H atom addition reactions to 1,3-pentadiene are compared to available C-3-C-5 alkenes and dienes, with external addition calculated to be kinetically favored over internal addition. However, the correlation between heats of formation and energy barriers for H atom addition to 1,2-dienes is different from that for 1,3- and 1,4-dienes. Hydrogen atom addition and abstraction rate constants are also compared for 1,3-pentadiene, with addition found to be dominant. The subsequent unimolecular reactions on the C5H9 PES are found to be highly complex with reactions taking place on a multiple-well multiple-channel PES. For clarity, the reaction mechanism and kinetics of each C5H9 radical are discussed individually in terms of the computed enthalpy of the reaction and activation, the transition-state structure/reaction class, and also in terms of the combustion species for which the reactions are of potential importance. The reactions on the C5H9 PES are divided into three reaction classes (H-shift isomerization, cycloaddition, and beta-scission reactions), and the reactivity-structure-based estimation rules for energy barriers are derived for these three reaction classes and compared to literature results for alkyl radicals.