Milano Card

Lots of advantages for short visits .
(Download and more information here)
The other categories are:
WiFi Network Finder
WiFi Map

Use this excellent app to find free available WiFi networks including Open WiFi Milano, the app also has other useful features. Read more about Open WiFi Milano here.
(Download for Android |iPhone)
Sightseeing
Spotted by Locals

The app has more than 70 city guides – including the one for Milan – and tells you what is worth seeing in the opinion of the people who live in Milan (also check out their blog here). Lots of great features.
(Download for Android | iPhone)
Grande Brera

With the opening of Palzzo Citterio as home for Pinacoteca Brera’s collection of modern art, the long planned Grande Brera is a reality and this app is essential for your visit to both museums
(Download for Android | iPhone)
Milan Travel Guide

A classic city-guide with the most important tourist attractions and it links text and maps.
Languages: English, Italian, Spanish, Russian and Chinese
(Download for Android | iPhone)
Milan Guide

Get Directions with offline maps and find out what attractions are near you at any given time
(Download for Android | iPhone)
Public transport
ATM Milano Official app

This is a very useful app for buying tickets, finding nearby stops and travel information.Remember to enable notifications so that you get updates in real time.
(Download for Android | iPhone)
Taxi
FreeNow (formerly MyTaxi)
You may need a taxi and can’t find any, with this app you can book one and pay with credit card directly in the app.
(Download for Android | iPhone)
Electric scooters and bicycles
Electrical scooters are a popular way to get around in Milan, watch out for yourself out there in traffic and be aware that wearing a helmet will soon be compulsory, you can not go over 20 km per hour, and where there are bicycle paths you have to go on them, otherwise you have to ride in the street to the right in the same direction as traffic (!) you are not allowed to ride on sidewalks, Scooters are only allowed in the centre of the city. Here are the apps you can download for Milan:

Helbiz (both scooters and bikes)
(Download for Android | iPhone)
Dott – your ride, your way (both scooters and bicycles)
(Download for Android | iPhone)
Tier (both scooters and bicycles)
(Download for Android | iPhone)
Lime (both scooters and bicycles)
(Download for Android | iPhone)
BIT (only sccoters)
(Download for Android | iPhone)
Car sharing
Car sharing is another popular way to get around in Milan and to and from Malpensa airport, the two that you can get all the way out there are;