Dielectric relaxation measurements have been used to study the crossover in dynamics with temperature and pressure, onset of breakdown of the Debye-Stokes-Einstein law, and the relation between the alpha and the beta relaxations in diethyl phthalate. The measurements made over 10 decades in frequency and a broad range of temperature and pressure enable the dc conductivity and the alpha- and the beta-relaxations to be studied altogether. The isobaric data show that the alpha-relaxation time tau(alpha) has temperature dependence that crosses over from one Vogel-Fulcher-Tammann-Hesse form to another at T(B)approximate to227 K and tau(alpha)approximate to10(-2) s. The dc conductivity sigma exhibits similar crossover at the same T-B. At temperatures above T-B, tau(alpha) and sigma have the same temperature dependence, but below T-B they become different and the Debye-Stokes-Einstein law breaks down. The breadth of the alpha relaxation is nearly constant for T<T-B, but decreases with increasing temperature for T>T-B. The time dependence of tau(beta) is Arrhenius, which when extrapolated to higher temperatures intersects tau(alpha) at T-beta nearly coincident with T-B. Isothermal measurements at various applied pressures when compared with isobaric data show that the shape of the alpha-relaxation depends only on tau(alpha), and not on the T and P combinations. At a constant temperature, while tau(alpha) increases rapidly with pressure, the beta-relaxation time tau(beta) is insensitive to applied pressure. This behavior is exactly the same as found in 1,1'-bis (p-methoxyphenyl) cyclohexane. The findings are discussed in the framework of the coupling model.