Quaternionic slice regular functions, introduced in 2006, are traditionally only studied over domains that are symmetric with respect to the real axis. This tradition initiated after some foundational results were published in 2009, such as the Representation Formula for axially symmetric domains. The talk will cover some new results concerning slice regular functions over domains that are not axially symmetric, including a Local Representation Formula. Such results allow to prove the next property, valid on the so-called simple domains: every slice regular function on a simple domain can be uniquely extended to the symmetric completion of its domain.