In solids, heat is usually carried by phonons or electrons. However, recent experiments on low-dimensional magnetic materials have revealed that magnetic excitations can substantially contribute to the thermal conductivity. In this work, thermal transport properties of one-dimensional spin-1/2 systems are studied within the framework of linear response theory. The main focus will be on two examples: the integrable XXZ chain and two-leg ladders. In the former case, the thermal conductivity diverges due to conservation laws, signaled by a finite thermal Drude weight. This quantity is studied as a function of temperature, magnetic field, and exchange anisotropy. In contrast to the XXZ chain, spin ladders and other generic spin models exhibit normal transport properties in the thermodynamic limit. A numerical analysis of the frequency dependence of the thermal conductivity is presented and a comparison with experimental data is suggested.