Abstract: The fundamental idea of Laser Wakefield Acceleration (LWFA) is reviewed. An ultrafast intense laser pulse drives coherent wakefield with a relativistic amplitude robustly supported by the plasma. While the large amplitude of wakefields involves collective resonant oscillations of the eigenmode of the entire plasma electrons, the wake phase velocity $\sim c$ and ultrafastness of the laser pulse introduce the wake stability and rigidity. A large number of worldwide experiments show a rapid progress of this concept realization toward both the high-energy accelerator prospect and broad applications. The strong interest in this has been spurring and stimulating novel laser technologies, including the Chirped Pulse Amplification, the Thin Film Compression, the Coherent Amplification Network, and the Relativistic Mirror Compression. These in turn have created a conglomerate of novel science and technology with LWFA to form a new genre of high field science with many parameters of merit in this field increasing exponentially lately. This science has triggered a number of worldwide research centers and initiatives. Associated physics of ion acceleration, X-ray generation, and astrophysical processes of ultrahigh energy cosmic rays are reviewed. Applications such as X-ray free electron laser, cancer therapy, and radioisotope production etc. are considered. A new avenue of LWFA using nanomaterials is also emerging.