At the outset, Deng famously told the Chinese to look out for themselves and seek a better life.

In recent years, millions have dramatically bettered their lives.

Still, hundreds of millions believe they have been left behind by China's breakneck pace of economic growth.

Disparities in income have never been wider.

Now, there is a raft of social, political and economic problems. Crime is rising in many Chinese cities. And one issue that makes the Chinese most angry is rampant corruption.

Since many in China are seeking to make money, the result is widespread nepotism, influence-peddling, bribes, ostentatious spending and misuse of public funds.

Yet leaders face the dilemma of having to demonstrate their resolve in curbing corruption while not tarnishing the Communist Party's image and threatening its legitimacy.

If the anti-graft campaign goes too far, analysts say, the party's image is tarnished and the stability of the leadership could be jeopardized.

One pundit puts it succinctly: "If you push anti-corruption through to the end, the Communist Party will die. If you don't, the country will die."

Some critics are no longer afraid to air grievances to local and central leadership. In recent months, they have taken desperate measures to seek redress.

On July 28, thousands of people in the eastern Qidong city in Jiangsu Province gathered in front of the city hall. Defying the police, they broke into the building in protest against a project to build a wastewater pipeline. Angry that the project could pollute their environment, they ransacked the government offices and man-handled senior city officials.

This incident is the latest in a series of recent embarrassments for the Chinese government -- signs, analysts say, of a fragile system fraying at its seams.

Other domestic factors, including environmental damage and slowing economic growth, all require Beijing's urgent attention.

Do current leaders have the skill, ideas and toughness to deal with them?

University of Alberta's Wenran Jiang said: "Ten years ago, when Hu Jintao and Wen Jiabao both came to power, what they first promised to the society was to fix some of the inequality issues. But ten years later, the issues have not gone away. Unless the new Party leadership can show that they can manage these problems, they will continue to face doubts from the general public."

China today has a few political and economic experiments underway, competing against each other.

With or without Bo Xilai, analysts say Beijing's leadership must find innovative and effective ways to govern a nation increasingly diverse and disunited after as a result of the 30 years of reform.