The diffusion-limited reaction was studied on a one-dimensional lattice in the presence of random fields and transition rates using Monte Carlo simulations. In the case of transition rates the hopping probabilities at a site are distributed according to the power law p(y)=nuy(nu-1) with 00 and A+B-->0 annihilation reactions. The exponent alpha(nu) depends on the disorder exponent nu. For A+A-->0, we found alpha(nu)=nu/(1+nu). For A+B-->0, we observed alpha=0.25 at nu>0.4 and alpha decreases monotonically for nu<0.4. In the case of the random fields the density decays according to C(t)similar to[b(E)/log(t)](2) regardless of the strength of the random fields E for A+A-->0 and A+A-->A reactions, where b(E)similar tolog[(1+E)/(1-E)]. The diffusion-limited coagulation A+A-->A belongs to the same universality class as the A+A-->0 reaction under the random fields. For A+B-->0 annihilations we observe that the density decays according to C(t)similar tob(E)/log(t) in the presence of the random fields.