Qiushi (求是) "Founded on July 1, 1988, Qiushi Journal is the organ of the Central Committee of the Communist Party of China (CPC). It is the most influential and authoritative magazine devoted to policy-making and theoretical studies, with a circulation of 1.26 million in 2010....The predecessor of Qiushi Journal was Hongqi (Red Flag), published from 1958 to 1988. The Chinese characters Hongqi were written by Chairman Mao Zedong. The Chinese characters Qiushi are in the handwriting of Deng Xiaoping and have become a striking logo of the magazine."
Red Flag (红旗文稿) is, along with Qiushi, now one of the signature publications of the CCP, although it was founded much more recently (in 2009). Published bi-weekly, it's focus is the propagation of political theory.
Party Building (党建) was founded in 1988, and the calligraphy used on its cover was written by Deng Xiaoping. The publication focuses on Party ideology and policy implementation. The latest issue and recent back issues can be found here. There is also an iPad app for the magazine that can be downloaded at the iTunes store.
Insight China (小康) comes from the Qiushi publishing house, and
Theory and Reform (理论与改革) is a monthly publication of the Sichuan Provincial Party School that focuses on applying Marxism to the problems surrounding the reform process.
Central Party School Journal (中央党校学报) is publishes quarterly by the Central Party School in Beijing. It covers current policy, initiatives such as the "One Belt One Road" as well as Party ideology.
Thought Politics Work Research (思想政治工作研究) is published monthly by the Central Propaganda Department and has been published beginning in 1983. As one would expect, its contents lean heavily towards ideology.
Front Line (前线) was first published in 1958, with the title calligraphy written by Peng Zhen. It halted publication during the Cultural Revolution and was restarted in 1981 under the name "Study and Research" (学习与研究), and in 1995 it returned to its original name. It leans heavily towards columns by scholars at the Party schools.
Theory Front (理论前沿) is a publication of the Central Party School in Beijing. As far as I can tell, it hasn't been updated since 2010.
Contemporary Party Member (当代党员) is a publication of Chongqing Municipal Party and looks to be a mouthpiece for Party members in the metropolis.
Party Member Digest (党员文摘) looks and reads remarkably similar to 青年文摘, albeit with a more stilted feel.