The past year has been a particularly busy one for insurance giant American International Group (AIG 0.90%). As we come closer to the beginning of 2014, investors should take some stock in the progress AIG has made over the course of 2013. Here are some of the biggest developments and events of AIG's 2013.

1.The beginning and end of government oversight
2013 marked the first months of AIG's freedom from governmental ownership, as the Federal Reserve sold off its remaining stake in the insurer in December 2012. With the reins fully back in its own hands, the company could now take on new goals and projects that it had been holding off on. The end of the government ownership was not to say that AIG was not under strict regulatory watch -- the Fed was still heavily involved in the oversight of the company's operations.

CEO Robert Benmosche cited the regulator's help in developing the testing methods it would need to perform with once the required performance metrics for Systemically Important Financial Institutions are finalized. The SIFI designation of AIG came in June, which was neither unexpected nor protested by AIG's management.

2. Flying high
December 2012 also marked the beginning of another process AIG has been dealing with all year: the divestiture of its International Leasing Finance Corp. to a group of Chinese buyers. Throughout 2013, the deal has hit roadblock after roadblock as the consortium looking to purchase the aircraft leasing business first had trouble coming up with the required deposit and then has endured a round of musical chairs as original members leave the group and new ones join.

AIG has been very patient with the entire ordeal, but as of its third-quarter conference call, management made it clear that a decision to close the deal as-is or walk away would need to be made in the fourth quarter. The company has been preparing a tangent line of attack for the disposal of ILFC (an IPO), but recent developments have shown that it is in talks with AerCap Holdings (AER 1.72%), the world's largest independent aircraft leasing business.

3. Business opportunities
AIG stepped out in two very different markets during 2013, the first being a new investment in China with the PICC Group. After the repayment of the government bailout made a sell-off of its stake in the AIA Group all but essential, AIG is reentering the People's Republic with a deal that first focused on property and casualty insurance products, with the potential to expand from there.

The second opportunity arose with the resurgence of the housing market. Though the company's near-collapse in 2008 was spurred on by risky bets on mortgage bonds, AIG stepped back into the mortgage guaranty ring in early 2013. The announcement made some investors nervous at first, but the company's strategy was different this time around -- and paid off in spades. The division has cleared off the majority of its bad loans from the financial crisis days and is going like gangbusters (much like the entire private mortgage insurance market).

4. Investors' favorite
Each and every quarter in 2013 so far has found AIG near the top of the hedge fund favorites list. Though there are some qualifications to the statement, AIG has been king of the hedge fund hill for most of the year. The importance of Wall Street's favoritism can't be understated as the catalyst for more and more investors returning to the beleaguered insurer.

Another top highlight for investors this year came after the second quarter closed, when management announced the reinstatement of a quarterly dividend. With a $0.10 dividend, the company only measured half of its pre-bailout dividend, but it was welcomed by investors who had waited for five years to see come capital returns. AIG also announced that it had approval to restart its share buyback program, which has been slow moving so far, but another welcomed event as investors look to have some of the dilution, caused by the governmental ownership, cut down.

5. Corporate tussles
AIG has been no stranger to the courtroom or boardroom this year. The insurer has both sought out fights with other companies and been the target of some serious pilfering. Bank of America (BAC 1.96%) was first on AIG's hit list this year, with the insurer going after the bank in two very costly court battles. Though the cases started earlier, big developments occurred during 2013 in both the $10 billion case over mortgage-backed securities and the $8.5 billion investor settlement over the same instruments.

Perhaps one of the most covered scuffles between AIG and another company came during the beginning of the year when four top executives defected in favor of a new segment at Berkshire Hathaway (BRK.B 1.19%). Though AIG made it clear that there was nothing to worry about, and that it had a "deep bench" of talent that would fill the spots, many investors worried that the exodus and the new competitng business from Berkshire Hathaway would hurt AIG deeply. To date, there hasn't been much proof showing the concerns were founded, but AIG did take a swipe at Berkshire in return: It canceled all plans to deal with Berkshire Hathaway's reinsurance businesses in the future, which could eventually come back to bite Berkshire in the future.

Busy, busy
This year has been a good one for the insurance behemoth. Not only is it firmly back on solid ground operations-wise, but it's returning value to its shareholders, taking a stand against other corporations, making progress on divestitures, and preparing for the future. As a long-term investor, you should feel confident that 2013 was a solid year of growth and development for the recovering company -- and that 2014 should be a banner year as well.