Regreso vs. vuelta vs. retorno

The Spanish words 'regreso', 'vuelta', and 'retorno' all convey the idea of returning or coming back but are used in different contexts and have subtle differences in meaning.

Regreso

'Regreso' refers to the action of returning to a place where we were before. It is commonly used in everyday conversation and can also denote the return journey from one location to another.
Mi regreso a casa fue tranquilo.
(My return home was peaceful.)
Los fans esperan el regreso del cantante.
(Fans are expecting the singer's return.)

Vuelta

'Vuelta' can also mean return, but it is usually used in more specific senses. It is often used to refer to returning to an original position or starting point and includes the idea of making a round trip.
Damos una vuelta en el parque.
(Let's take a tour around the park.)
Estoy esperando su vuelta del trabajo.
(I'm waiting for her to come back from work.)

Retorno

'Retorno' is more formal than 'regreso'. It usually refers to returning or going back often with a sense of finality or after a long time. It also denotes recurrence in cyclical phenomena.
El retorno del rey marcó un nuevo comienzo para el reino.
(The king's return marked a new beginning for the kingdom.)
El ciclo de retorno del cometa es de 76 años.
(The comet's return cycle is 76 years.)

Summary

Though 'regreso', 'vuelta', and 'retorno' in Spanish all mean 'return', they are used differently. 'Regreso' implies coming back to where one was before, 'vuelta' refers more broadly to circling back or making a round trip, and 'retorno' signifies return often after a long time or with finality.