Next-generation wireless networks are designed to

provide reliable and high data-rate communication services for

diverse scenarios, such as vehicle-to-vehicle, unmanned aerial

vehicles and satellite networks. The severe Doppler spreads in

the underlying time-varying channels induce destructive intercarrier

interference (ICI) in the extensively adopted orthogonal

frequency division multiplexing (OFDM) waveform, leading to

severe performance degradation. This calls for a new air interface

design that can accommodate the severe delay-Doppler

spreads in highly dynamic channels while possessing sufficient

flexibility to cater to various applications. This article provides

a comprehensive overview of a promising chirp-based waveform,

named affine frequency division multiplexing (AFDM). It features

two tunable parameters and achieves optimal diversity order in

doubly dispersive channels (DDC). We study the fundamental

principle of AFDM, illustrating its intrinsic suitability for DDC.

Based on that, several potential applications of AFDM are

explored. Furthermore, the major challenges and the corresponding

solutions of AFDM are presented, followed by several

future research directions. Finally, we draw some instructive

conclusions about AFDM, hoping to provide useful inspiration

for its development.