Can I use
?

Service Workers

- CR

Method that enables applications to take advantage of persistent background processing, including hooks to enable bootstrapping of web applications while offline.

IE

  1. 5.5 - 10: Not supported
  2. 11: Not supported

Edge

  1. 12 - 14: Not supported
  2. 15 - 16: Disabled by default
  3. 17 - 87: Supported
  4. 88: Supported

Firefox

  1. 2 - 32: Not supported
  2. 33 - 43: Disabled by default
  3. 44: Supported
  4. 45: Supported
  5. 46 - 51: Supported
  6. 52: Supported
  7. 53 - 59: Supported
  8. 60: Supported
  9. 61 - 67: Supported
  10. 68: Supported
  11. 69 - 84: Supported
  12. 85: Supported
  13. 86 - 87: Supported

Chrome

  1. 4 - 39: Not supported
  2. 40 - 44: Partial support
  3. 45 - 87: Supported
  4. 88: Supported
  5. 89 - 91: Supported

Safari

  1. 3.1 - 11: Not supported
  2. 11.1 - 13.1: Supported
  3. 14: Supported
  4. TP: Supported

Opera

  1. 9 - 26: Not supported
  2. 27 - 31: Partial support
  3. 32 - 72: Supported
  4. 73: Supported

iOS Safari

  1. 3.2 - 11.2: Not supported
  2. 11.3 - 13.7: Supported
  3. 14: Supported

Opera Mini

  1. all: Not supported

Android Browser

  1. 2.1 - 4.4.4: Not supported
  2. 81: Partial support

Opera Mobile

  1. 10 - 12.1: Not supported
  2. 59: Partial support

Chrome for Android

  1. 88: Supported

Firefox for Android

  1. 85: Supported

UC Browser for Android

  1. 12.12: Supported

Samsung Internet

  1. 4 - 12.0: Supported
  2. 13.0: Supported

QQ Browser

  1. 10.4: Supported

Baidu Browser

  1. 7.12: Partial support

KaiOS Browser

  1. 2.5: Not supported

Details on partial support can be found on is ServiceWorker Ready?

Resources:
MDN Web Docs - Service Workers
List of various resources
HTML5Rocks article (introduction)