Scanning thermal microscope-detected ferromagnetic resonance (SThM-FMR) combines a thermal near-field microscope with a FMR spectrometer and detects the thermal response due to resonant microwave absorption by measuring the resistivity change in the thermal nanoprobe. The advantage of this technique is to provide imaging capabilities at fixed resonance conditions as well as local microwave spectroscopy at the nanoscale. A technique that uses the same setup but detects the thermoelastic response of the sample is the scanning thermoelastic microscope-detected FMR (SThEM-FMR). This latter technique is advantageous when FMR spectra of single nanostructures have to be recorded at a fixed position. The experimental setups and the signal generation processes of SThM/SThEM-FMR are described in detail. With the SThM-FMR setups a temperature resolution of 1 mK and a local resolution of 30 nm are actually achieved. With SThEM-FMR the obtained local resolution is 10 nm. The detection limits of both techniques can be as low as 10(6) spins. To demonstrate the potential of these new techniques SThM/SThEM-FMR investigations of local magnetic anisotropies, magnetization dynamics of single nanodots and inhomogeneous FMR excitations due to finite size effects are presented. Simultaneously, information on the magnetic parameters, the topography, and the thermal properties is provided. To describe the further potential of this recently developed SThM-FMR technique, combined magnetoresistance and FMR investigations are presented and an outlook on possible future applications is given.