In the yeast Hansenula polymorpha the development and turnover of peroxisomes is readily achieved by manipulation of the cultivation conditions. The organelles massively develop when the cells are incubated in the presence of methanol as the sole source of carbon and energy. However, they are rapidly and selectively degraded when methanol-grown cells are placed at conditions of repression of methanol metabolism (e.g. in glucose or ethanol excess conditions) by a process termed macropexophagy. Degradation of peroxisomes is also observed when the cells are placed at nitrogen-depletion conditions (microautophagy). This contribution details the methodologies that are currently in use investigating macropexophagy and microautophagy in H. polymorpha. Emphasis is placed on various structural (fluorescence microscopy, electron microscopy) and biochemical (specific enzyme activity measurements, Western blotting) approaches.