Steam distillation is by far the most common form of essential oil extraction but there are other methods including enfleurage, expression, maceration and solvent extraction.
The method used depends on the part of the plant the essential oil is to be extracted from. For example, the delicate flower petals of roses, jasmine and neroli often requires enfleurage and sometimes maceration or solvent extraction.
Expression is often used for the rind of certain citrus fruit including lemons, oranges and grapefruit.
The steam distillation methods works well with leaves, seeds, roots, flowers and stems.
You can find out more details about the various methods of Essential Oil Extraction here.