A very simple date time ago file in swift inspired from kevinlawler's "NSDate-TimeAgo".

DateTimeAgo.swift

//
//  DateTimeAgo.swift
//
//  Created by Patrick Taylor on 30/01/2016.
//  Copyright © 2016 Patrick Taylor. All rights reserved.
//

import Foundation
import Darwin

func dateTimeAgo(date: Date) -> String {

    let deltaSeconds = secondsFrom(date: date)
    let deltaMinutes:Double = Double(deltaSeconds / 60)

    if deltaSeconds < 5 {
        return "Just now"
    }
    if deltaSeconds < 60 {
        return String(deltaSeconds) + " seconds ago"
    }
    if deltaSeconds < 120 {
        return "A minute ago"
    }
    if deltaMinutes < 60 {
        return String(Int(deltaMinutes)) + " minutes ago"
    }
    if deltaMinutes < 120 {
        return "An hour ago"
    }
    if deltaMinutes < (24 * 60) {
        let hours = flooredString(delta: deltaMinutes, dividedBy: 60)
        return hours + " hours ago"
    }
    if deltaMinutes < (24 * 60 * 2) {
        return "Yesterday"
    }
    if deltaMinutes < (24 * 60 * 7) {
        let days = flooredString(delta: deltaMinutes, dividedBy: (60 * 24))
        return days + " days ago"
    }
    if deltaMinutes < (24 * 60 * 14) {
        return "Last week"
    }
    if deltaMinutes < (24 * 60 * 31) {
        let weeks = flooredString(delta: deltaMinutes, dividedBy: (60 * 24 * 7))
        return weeks + " weeks ago"
    }
    if deltaMinutes < (24 * 60 * 61) {
        return "Last month"
    }
    if deltaMinutes < (24 * 60 * 365.25) {
        let months = flooredString(delta: deltaMinutes, dividedBy: (60 * 24 * 30))
        return months + " months ago"
    }
    if deltaMinutes < (24 * 60 * 731) {
        return "Last year"
    }

    let years = flooredString(delta: deltaMinutes, dividedBy: (60 * 24 * 365))
    return years + " years ago"
}

private func secondsFrom(date:Date) -> Int {
    return Calendar.current.dateComponents([.second], from: date, to: Date()).second ?? 0
}

private func flooredString(delta: Double, dividedBy: Double) -> String {
    return String(Int(floor(delta/dividedBy)))
}

Updated to Swift 3.0

👍