Muthuramakrishnan gives a talk “On Adaptively Secure Protocols”. He introduces two main results; first a compiler which can transform a semi-honest and statically secure MPC protocol to an adaptively UC-secure protocol, with only a constant increase in rounds in its execution and minimal setup assumptions (such as a Common Reference String). The second result is the first concurrent non-malleable zero knowledge (CNMZK) protocol secure in the fully adaptive setting. As an artifact of the second result Muthu also provides a compiler which takes any semi-honest secure protocols as input and outputs a fully concurrently secure protocol under polytime assumptions in the Angel-Based UC-framework.
The motivations for considering adaptive adversaries are many, first of all because it yields stronger security and leakage resilience. In the more practical setting it yields applications in cloud computing.
To get the first result Muthu uses simulatable public key encryption and UC puzzles. He furthermore uses non-mallable commitments in his construction.
To achieve the second result Muthu overcomes an impossibility result by tweaking the definitions used a little bit.
The details and tricks are plentiful and not that easily explained in a blog post, so I direct the interested reader to the paper.