I will discuss the particle acceleration by turbulence,
and its application to blazars, GRBs and pulsar wind nebulae (PWNe).
The magnetic fields in blazars and PWNe are subdominant component
compared to the accelerated electrons. In such a weakly magnetized plasma,
fast mode MHD waves can be responsible for the particle acceleration.
The acceleration timescale is comparable to the dynamical timescale,
so that the time-dependent treatment is indispensable to obtain the
particle energy distribution. Our models reproduce the hard spectra
of blazars and PWNe. This process may be important for interfering
the electron cooling in GRBs.