Two classic radio-frequency (RF) plasmas, i.e., the capacitively and the inductively coupled plasma (CCP and ICP), are widely employed in material processing, e.g., etching and thin film deposition, etc. Since RF plasmas are usually operated in particular circumstances, e.g., low pressures (mTorr ~ Torr), high-frequency electric field (13.56 MHz ~200 MHz), reactive feedstock gases, diverse reactor configurations, etc., a variety of physical phenomena, e.g., electron resonance heating, discharge mode transitions, striated structures, standing wave effects, etc., arise. These physical effects could significantly influence plasma-based material processing. Therefore, understanding the fundamental processes of RF plasma is not only of fundamental interest, but also of practical significance for the improvement of the performance of the plasma sources. In this article, we review the major progresses that have been achieved in the fundamental study on the RF plasmas, and the topics include 1) electron heating mechanism, 2) plasma operation mode, 3) pulse modulated plasma, and 4) electromagnetic effects. These topics cover the typical issues in RF plasma field, ranging from fundamental to application.