Google App Script (https://script.google.com/home) to automatically archive or delete emails. I use it to manage email from lists that I don't want to unsubscribe from but I want to prevent from building up forever in my inbox. Add a trigger to have it run every day. It emails me a summary of its actions, and it deletes old copies of that email!

mailCleanup.gs

var totalCount = 0;

// Entry point must be named doGet for HTTP GET and doPost for HTTP POST
function doGet() {
  return mailCleanup()
}

// Define mail filters, perform actions (archive or delete) on each one, send email report when done
function mailCleanup() {
  var blastSenders = ['from:[email protected]',
                      'from:[email protected]',
                      'from:banana',
                      '((from:hamilton lottery AND unfortunately) OR subject:"lottery entry received")];
  var msg = 'Daily blasts older than 3 days:\n    • ' + actOnMail('(' + blastSenders.join(' OR ') + ') AND in:inbox AND older_than:3d', 'delete')
  msg += '\nSocial older than 30 days:\n    • ' + actOnMail('category:social AND in:inbox AND older_than:30d', 'archive')
  msg += '\nPromotions older than 30 days:\n    • ' + actOnMail('category:promotions AND in:inbox AND older_than:30d', 'delete')
  msg += '\nUpdates older than 14 days:\n    • ' + actOnMail('category:updates AND in:inbox AND older_than:14d', 'archive')
  GmailApp.sendEmail('[YOUR EMAIL ADDRESS HERE]', 'Mail Cleanup Report - ' + totalCount + ' messages cleaned', msg)
  actOnMail('subject:"mail cleanup report" in:inbox older_than:5d', 'delete') // don't report on this one
  Logger.log(msg)
  return ContentService.createTextOutput(msg)
}

// Perform the actual gmail search and archive/delete resultset as requested
function actOnMail(filter, action) {
  var maxThreads = 100
  var msgCount = 0
  while(true) {
    var staleThreads = GmailApp.search(filter, 0, maxThreads)
    msgCount += staleThreads.length
    if(staleThreads.length > 0) {
      Logger.log('Found ' + staleThreads.length.toString() + ' stale messages. Cleaning them now . . .')
      var autoCleanedLabel = GmailApp.getUserLabelByName("autocleaned")
      autoCleanedLabel.addToThreads(staleThreads)
      switch(action)
      {
        case 'archive':
          GmailApp.moveThreadsToArchive(staleThreads)
          break
        case 'delete':
          GmailApp.moveThreadsToTrash(staleThreads)
          break
        default:
          Logger.log('Unknown action \'' + action + '\'! Ignoring it!')
          break
      }
    } else {
      break
    }
  }
  
  totalCount += msgCount
  var msg = msgCount.toString() + ' stale messages have been labeled \'autocleaned\' and ' + action + 'd.'
  Logger.log(msg)
  return msg
}