Notable progresses have recently been made in quantitative scanning thermal microscopy (SThM) based on a sub-micron thermocouple junction fabricated on an atomic force microscopy (AFM) tip. Here, the underlying theoretical basis for such measurements is re-examined, with a focus on the effects of the temperature and spatial dependences of the interface thermal conductance. The nature of the temperaure being measured is discussed in relationship with the phonon transmission coeffiicient across the tip-sample gap. Comparison is made between the results obtained form the SThM and Raman thermal mapping measurements. The SThM method has recently been employed to study heat dissipation in emerging electronic devices made of various two-dimensional (2D) materials. In addition, a different type of scanning thermal probe with a resistive heater and thermometer near the tip has been used to measure thermal transprot across a point contact, and an attempt is made to use a scanning thermoelectric microscopy method to probe the variation of the local thermoelectric property near the edges of 2D materials.