This paper focuses on several major theoretical problems of modern political economics, such as "negative value" of joint production, the law of changes in commodity value, the transformation of values, the law of the decline in average margin, economic long waves, fairness and efficiency, international unequal exchange and virtual economy & value. And based on these issues, along with these key points around new theories of value theory, economic growth and economic cycle, income distribution and international change inequality, the macroeconomic framework of virtual value and its application, it summarizes core views of the challenges and defense on these problems as well as some new thinking and exploration in domestic and foreign academia. As the new theory of value theory is concerned, and based on "Steedman interrogation", it raises "negative theory" in environmental field; in response to "the mystery of the century", it explores the law of changes in commodity value under the background of competition and monopoly,heterogeneous goods of the same kind, and joint production; faced with the transformation problem for a century on the basis of one-sided viewpoint, it demonstrates dynamic transformation model. In terms of economic growth and economic cycle, to critique "Okishio theorem", it establishes the theoretical mode of a technical and institutional organic composition (TICC); based on the problem of comparison between three long-wave theories, it establishes a long-wave theory according to technology power, system power and coupling power. As for income distribution and international exchange inequality, according to "converse" phenomenon of income distribution, it demonstrates the theoretical analysis by bringing opportunity inequality into Marxist income distribution theoretical framework; according to the new changes in the unequal international exchange in the three areas of international economy, it builds the international inequality blend theory. As for virtual value and virtual economy, it builds a theoretical model of virtual economy and applies it into areas such as "Internet Plus", "Bitcoin", and "new media".