The short answer is yes, at least for the audio and microphone, especially for newer Android phone models. However, volume controls are generally not compatible across different smartphone brands and operating systems.

If you are curious about more technical details, please read on. Most headsets for smartphones have four conductors, referred to as TipRing 1Ring 2, and Sleeve (TRRS), respectively. 

The former two conductors are mapped to the left and right audio channels. For ring 2 and sleeve, there are two different standards:

  • CTIA / AHJ, which maps ring 2 and sleeve to ground and microphone, respectively. This includes Apple devices, most Android devices (including HTC, latest Samsung), new Nokia, Microsoft (including surface, lumia, and Xbox one controller w/ chat adapter), Sony (Dualshock 4), etc.
  • OMPT, which maps ring 2 to sleeve to microphone and ground, respectively. This includes old Nokia (including Lumia series), old Samsung (2012 Chromebooks), old Sony Ericsson (2010 and 2011 Xperias) and Sony (PlayStation Vita).

You cannot use the 4-pole headsets made for CITA/AHJ standard on phones with the OMPT standard, or vice versa. However, since Apple devices and most newer Android devices all use the CITA / AHJ standard, they are compatible for audio and microphone. However, volume controls are generally controlled by software which makes them incompatible across different smartphone brands and operating systems.