What are the recent developments affecting the doctrine of privity in
the law of contract?

You should name your city, state and country. Powerful forces are at
work to deprive both individuals and groups of rights of privacy. The
tax collector, the enviornmentalist, the bureaucracy and lawyers all
want to micro manage your contract. Computer technology is making it
easy and inexpencive to learn the details of secret contracts. Some
examples or specifics would be helpful.   Neil

The question actually asks about ~privity~, not privacy.  That
doctrine relates to understanding which parties stand in relationship
to one another such that the terms of the contract are biding on them,
e.g., if you buy a toaster at a large retailer, are you in privity
under the sales contract with the retailer or the toaster
manufacturer?  Another example: if you buy software at a large
retailer, under your end user license agreement is the licensor the
retailer or the manufacturer?  You would have contractual privity with
the licensor, whoever that was as defined in the EULA.  Privity is
important because without it a person cannot, generally speaking,
enjoy the benefits of a contract.

What types of contracts are we talking about, abid3583?  Privity is
very rapidly evolving in the law of online contracts, but it has
changed very little recently in the realm of real estate contracts. 
Please advise.