So I know this is an older question but I think it could stand an updated answer.

Microsoft has officially released asp.net vnext and its open source and deploy-able to both Linux and Mac. Its all still pretty new but does rely on the latest builds of mono and thus currently needs you to compile the mono-framework but in time I suspect that it will be easier to access as various linux distros release updated versions of mono. This is a how to setup guide

This information may be somewhat volatile and with updates is due to change.

Update ASP.NET CORE 11/10/2017

• asp.net vnext is now known as asp.net core.
• asp.net core is being treated as a high priority in Microsoft due in part to its use with microservice architecture and docker and container technologies
• It has become much more compatible with existing .net libraries due to .net standard 2.0.
• It performs well when compared to other technology stacks such as go and node.js