  In 1965 it was discovered that cosmic ray air showers emit impulsive radio
signals at frequencies below 100 MHz. After a period of intense research in the
1960s and 1970s, however, interest in the detection technique faded almost
completely. With the availability of powerful digital signal processing
techniques, new attempts at measuring cosmic ray air showers via their radio
emission were started at the beginning of the new millennium. Starting with
modest, small-scale digital prototype setups, the field has evolved, matured
and grown very significantly in the past decade. Today's second-generation
digital radio detection experiments consist of up to hundreds of radio antennas
or cover areas of up to 17 km$^{2}$. We understand the physics of the radio
emission in extensive air showers in detail and have developed analysis
strategies to accurately derive from radio signals parameters which are related
to the astrophysics of the primary cosmic ray particles, in particular their
energy, arrival direction and estimators for their mass. In parallel to these
successes, limitations inherent in the physics of the radio signals have also
become increasingly clear. In this article, we review the progress of the past
decade and the current state of the field, discuss the current paradigm of the
radio emission physics and present the experimental evidence supporting it.
Finally, we discuss the potential for future applications of the radio
detection technique to advance the field of cosmic ray physics.
