The article addresses the formation mechanisms of naphthalene and indene, which represent prototype polycyclic aromatic hydrocarbons (PAH) carrying two six-membered and one five- plus a six-membered ring. Theoretical studies of the relevant chemical reactions are overviewed in terms of their potential energy surfaces, rate constants, and product branching ratios; these data are compared with experimental measurements in crossed molecular beams and the pyrolytic chemical reactor emulating the extreme conditions in the interstellar medium (ISM) and the combustion-like environment, respectively. The outcome of the reactions potentially producing naphthalene and indene is shown to critically depend on temperature and pressure or collision energy and hence the reaction mechanisms and their contributions to the PAH growth can be rather different in the ISM, planetary atmospheres, and in combustion flames at different temperatures and pressures. Specifically, this paradigm is illustrated with new theoretical results for rate constants and product branching ratios for the reaction of phenyl radical with vinylacetylene. The analysis of the formation mechanisms of naphthalene and its derivatives shows that in combustion they can be produced via hydrogen-abstraction-acetylene-addition (HACA) routes, recombination of cyclopentadienyl radical with itself and with cyclopentadiene, the reaction of benzyl radical with propargyl, methylation of indenyl radical, and the reactions of phenyl radical with vinylacetylene and 1,3-butadiene. In extreme astrochemical conditions, naphthalene and dihydronaphthalene can be formed in the C6H5 + vinylacetylene and C6H5 + 1,3-butadiene reactions, respectively. Ethynyl-substituted naphthalenes can be produced via the ethynyl addition mechanism beginning with benzene (in dehydrogenated forms) or with styrene. The formation mechanisms of indene in combustion include the reactions of the phenyl radical with C3H4 isomers allene and propyne, reaction of the benzyl radical with acetylene, and unimolecular decomposition of the 1-phenylallyl radical originating from 3-phenylpropene, a product of the C6H5 + propene reaction, or from C6H5 + C3H5.