Recent developments of coherent terahertz (THz) oscillators based on the intrinsic Josephson junctions (IJJs) in mesas of the high temperature superconductor Bi2Sr2CaCu2O8+δ are reviewed. Experimental and theoretical studies of the emission from equilateral, right-angled isosceles, and acute isosceles triangular mesas are compared with those obtained from rectangular, square, and disk mesas, in order to determine the role of the mesa geometry. The superconducting properties and emission frequency f spectra are presented for a variety of triangular mesa geometries. Analytic and finite difference time domain numerical calculations of the emissions from the internal electromagnetic (EM) cavity modes of triangular mesas are compared with experiment. The experimental f always satisfies the ac Josephson relation, and its narrow linewidth arises from the synchronized emissions from many IJJs. For some mesa geometries, f also strongly locks onto an EM cavity mode frequency, enhancing the emission’s stability and output power. For other geometries, such cavity mode locking is weak, and f is highly tunable.