Visa Processing Times
UKVI has released a site wizard called Visa processing times that provides the expected turn-around for each issuing post by visa type.
The user can enter the relevant issuing post and visa type and is then given historical data broken out by processing time. A sample for Paris looks like...
People wanting to how the status of their application can use this wizard to get an estimate based upon historical data.
The original answer is also accurate and does not need to be changed as a result of this update. Email/SMS updates for certain types of applications at certain issuing posts are still available to applicants.
Email and SMS Alerts
The most recent SMS you received is your status, and when it changes you will be notified via SMS. Many people find that the SMS facility is not granular enough to suit their needs, especially when they are awaiting important news, but there's actually no other way to learn more. Their internal systems only have about 5 status's anyway.
Your T2 sponsor, on the other hand has access to the UKVI Sponsor Management System and can query the database on your behalf. The only information that your sponsor is likely to get is what you already received via SMS. The same goes for your VFS, but they cannot access Sponsor Management.
Of these, your best option is to await the next SMS from them.
Starting in January 2015, they will initiate a programme to advise IN COUNTRY applicants of their status by email. So your renewal or subsequent applications can take advantage of that method.
Outliers and Exceptions
UKVI has agreed a service level with Parliament and as long as your application falls within their agreed time limit, they are not obliged to provide extraordinary status info. Once they have exceeded the time limit and they have not reached a decision, they will notify you. Also at that point you have the option of initiating a query on your own. This holds true for all visa applications across the board, but each visa type has a different target.
It is also possible to learn detailed status via an MP who expresses interest. This is arguably the very worst alternative because their response has to go through the Ministerial Correspondence Unit, which takes a long time and your processing clock reverts back to square one. And all the response will say is that your application is awaiting a decision and reference the appropriate service level.