Phase transitions are a physical phenomenon known by mankind from its very beginning 200,000 years ago with the transition of water from solid ice to liquid water to gaseous steam. But the transitions between these so called states of matter are not the only phase transitions, there are a lot more, and amongst them we find the transition between the ferromagentic and paramagnetic phase of magnetic materials as well as the crystallographic martensitic phase transition. These two phase transitions are associated with microscopic structural changes and this makes them very interesting candidates for detailed investigations with a transmission electron microscope. The materials whose phase transitions are investigated in this thesis are the diluted magnetic semiconductor (Ga, Mn)As and diluted iron-palladium alloys which become ferromagnetic at low temperatures as well as niobium-3-tin which undergoes a structural transition