Zebra Crossing is a software development company based in New Zealand that specializes in mobile app development. They use tools like ASP.Net, MVC, C#, and SQL Server for websites and follow an Agile development process. For mobile apps, they recommend either mobile websites, hybrid/HTML5 apps, or native apps developed using Xamarin which allows sharing code across platforms. They provide an example of their app "The Happiness App" which was developed for iPhone using Xamarin in 120 hours.