Here is a list of all known Navy battles since 1980:
1980 - Operation Morvarid - Iranian navy decisively defeats Iraqi navy (Destruction of 80% of the Iraqi Navy).
1982 - Battle of Seal Cove - Falklands War. A minor naval clash, it involves the attempt by two Royal Navy frigates to seize an Argentine Navy coaster. The coaster evaded capture by running aground.
1986 - Action in the Gulf of Sidra (1986) - US Navy engages Libyan Navy in a fleet action.
1988 - April 18 Operation Praying Mantis - In the largest US naval engagement since World War II, the U.S. Navy defeats Iranian naval forces in retaliation for the mining of the USS Samuel B. Roberts during a patrol mission.
1991 - January 29 - February 2 - The Battle of Bubiyan where Coalition warships and aircraft destroy the bulk of the Iraqi Navy.
1998 - February 23 - The Sri Lankan Navy and LTTE Sea Tigers clash off Sri Lanka, killing more than 60.
1999 - June 9–15 First Battle of Yeonpyeong South Korean flotilla defeats North Korean flotilla.
21st century
2001 - December 22 Battle of Amami-Ōshima Japanese coast guard vessels sink an armed North Korean spy trawler.
2002 - June 29 Second Battle of Yeonpyeong A South Korean naval patrol encounters North Korean intruders and force them to withdraw.
2006 - May 11 - The Sri Lankan Navy and LTTE Sea Tigers clash, leaving 18 SLN personnel and 4-30 Tigers dead
2008 - August 9 - The Russian Navy's Black Sea Fleet sinks a Georgian Navy ship during the Battle off the coast of Abkhazia
2009 - November 10 Battle of Daecheong A South Korean patrol damages a North Korean gunboat forcing it to withdraw.
2011 - May 12 - Canadian, British, and French ships repulse a Libyan naval attack on the city of Misrata.
Engineering Casualty
The Littoral Combat Ships last year have all experienced significant engineering casualties, so you have a greater chance of learning more about that.
USS Coronado
USS Freedoom
USS Milwaukee
USS Fort Worth
USS Montgomery
USS Zumwalt
Is there something specific about these kinds of situations you want to ask about?