We can use transformers to carry out impedance matching. However, using various configurations of BJT circuit can achieve the same effect. Here I am talking about common collector, common base and common emmiter configurations. In different configurations we get different input output impedances that can be controlled to much extent.
When do we use a transformer to match impedances and when do we use other circuitry. I understand that if we have very high power applications than transofmer can provide isolation, but what about other not so high voltage applications?
I'd use a transformer when I want to isolate one signal from another. The transformer provides galvanic separation between two circuits and this is needed in several applications. One that springs to mind is a data coupler between a rotating machine and a static data receiver - you can't use wires but, you can use a rotating transformer to couple the data.
I've used near-field data transfer of modulated data as well and, in effect, antennas have become a transformer.
You can find RS485 chips that now embody isolation transformers and, ADI have a series of data coupling chips that incorporate tiny transformers to provide galvanic isolation.