A reflexive and symmetric binary relation on a set is called a tolerance. A tolerance T on a semigroup S is called left compatible if (x,y)\(\in T\Rightarrow (zx,zy)\in T\) for all \(z\in S\), right compatible if (x,y)\(\in T\Rightarrow (xz,yz)\in T\) for all \(z\in S\), weakly compatible if it is simultaneously right compatible and left compatible, compatible if (x,y)\(\in T\&(u,v)\in T\Rightarrow (ux,vy)\in T\). Let LC (or RC) be the class of all semigroups on which every tolerance is left (or right respectively) compatible. The paper gives a complete characterization of LC and RC (the case of a band and of a semigroup not being a band are distinguished). At the end it is proved that every tolerance on a semigroup S is weakly compatible if and only if every tolerance on S is compatible. A characterization of semigroups with this property is given.