Quick Overview
Please note that there are different common names for this artifact.

Flow effects in MRI produce a range of artifacts, e.g. intravascular signal void by time of flight effects; turbulent dephasing and first echo dephasing, caused by flowing blood.
Through movement of the hydrogen nuclei (e.g. blood flow), there is a location change between the time these nuclei experience a radio frequency pulse and the time the emitted signal is received (because the repetition time is asynchronous with the pulsatile flow).
The blood flow occasionally produces intravascular high signal intensities due to flow related enhancement, even echo rephasing and diastolic pseudogating. The pulsatile laminar flow within vessels often produces a complex multilayered band that usually propagates outside the head in the phase encoded direction. Blood flow artifacts should be considered as a special subgroup of motion artifacts.

Artifacts can be reduced by reduction of phase shifts with flow compensation (gradient moment nulling), suppression of the blood signal with saturation pulses parallel to the slices, synchronization of the imaging sequence with the heart cycle (cardiac triggering) or can be flipped 90° by swapping the phase//frequency encoding directions.

See also Flow Related Enhancement and Flow Effects.

(FID) A free induction decay curve is generated as excited nuclei relax. The amplitude of the FID signal becomes smaller over time as net magnetization returns to equilibrium. If transverse magnetization of the spins is produced, e.g. by a 90° pulse, a transient MR signal will result that will decay toward zero with a characteristic time constant T2 (or T2*); this decaying signal is the free induction decay.
The signal peaks of the echoes fall onto this T2 decay curve, while at each echo the signals arise and decay with T2*. The typical T2 relaxation times being of the order of 5-200 ms in the human body. The first part of the FID is not observable (named the 'receiver dead time') caused by residual effects of the powerful exciting radio frequency pulse on the electronics of the receiver.

(GRE - sequence) A gradient echo is generated by using a pair of bipolar gradient pulses. In the pulse sequence timing diagram, the basic gradient echo sequence is illustrated. There is no refocusing 180° pulse and the data are sampled during a gradient echo, which is achieved by dephasing the spins with a negatively pulsed gradient before they are rephased by an opposite gradient with opposite polarity to generate the echo.
See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The excitation pulse is termed the alpha pulse α. It tilts the magnetization by a flip angle α, which is typically between 0° and 90°. With a small flip angle there is a reduction in the value of transverse magnetization that will affect subsequent RF pulses. The flip angle can also be slowly increased during data acquisition (variable flip angle: tilt optimized nonsaturation excitation). The data are not acquired in a steady state, where z-magnetization recovery and destruction by ad-pulses are balanced. However, the z-magnetization is used up by tilting a little more of the remaining z-magnetization into the xy-plane for each acquired imaging line.
Gradient echo imaging is typically accomplished by examining the FID, whereas the read gradient is turned on for localization of the signal in the readout direction. T2* is the characteristic decay time constant associated with the FID. The contrast and signal generated by a gradient echo depend on the size of the longitudinal magnetization and the flip angle. When α = 90° the sequence is identical to the so-called partial saturation or saturation recovery pulse sequence. In standard GRE imaging, this basic pulse sequence is repeated as many times as image lines have to be acquired. Additional gradients or radio frequency pulses are introduced with the aim to spoil to refocus the xy-magnetization at the moment when the spin system is subject to the next α pulse.
As a result of the short repetition time, the z-magnetization cannot fully recover and after a few initial α pulses there is an equilibrium established between z-magnetization recovery and z-magnetization reduction due to the α pulses.
Gradient echoes have a lower SAR, are more sensitive to field inhomogeneities and have a reduced crosstalk, so that a small or no slice gap can be used. In or out of phase imaging depending on the selected TE (and field strength of the magnet) is possible. As the flip angle is decreased, T1 weighting can be maintained by reducing the TR. T2* weighting can be minimized by keeping the TE as short as possible, but pure T2 weighting is not possible. By using a reduced flip angle, some of the magnetization value remains longitudinal (less time needed to achieve full recovery) and for a certain T1 and TR, there exist one flip angle that will give the most signal, known as the "Ernst angle".
Contrast values:
PD weighted: Small flip angle (no T1), long TR (no T1) and short TE (no T2*)
T1 weighted: Large flip angle (70°), short TR (less than 50ms) and short TE
T2* weighted: Small flip angle, some longer TR (100 ms) and long TE (20 ms)

Classification of GRE sequences can be made into four categories:

• T1 weighted or incoherent/(RF or gradient) spoiled GRE sequences
• T1/T2* weighted or coherent/refocused GRE sequences
• T2 weighted contrast enhanced GRE sequences
• ultrafast GRE sequences

See also Gradient Recalled Echo Sequence, Spoiled Gradient Echo Sequence, Refocused Gradient Echo Sequence, Ultrafast Gradient Echo Sequence.

Gradient moment nulling used as motion artifact suppression technique (MAST) reduces constant velocity motion distortion in standard spin echo or gradient echo pulse sequences. It is an adjustment to zero at the echo time (TE) of the net moments of the amplitude of the waveform of the magnetic field gradients with time. The zeroth moment is the area under the curve. The first moment is the 'center of gravity' etc.
The aim is to minimize the phase shifts acquired by the transverse magnetization of excited nuclei moving along the gradients (including the effect of refocusing radio frequency pulses), particularly for the reduction of image artifacts due to motion.

(IR) The inversion recovery pulse sequence produces signals, which represent the longitudinal magnetization existing after the application of a 180° radio frequency pulse that rotates the magnetization Mz into the negative plane. After an inversion time (TI - time between the starting 180° pulse and the following 90° pulse), a further 90° RF pulse tilts some or all of the z-magnetization into the xy-plane, where the signal is usually rephased with a 180° pulse as in the spin echo sequence. During the initial time period, various tissues relax with their intrinsic T1 relaxation time.
In the pulse sequence timing diagram, the basic inversion recovery sequence is illustrated. The 180° inversion pulse is attached prior to the 90° excitation pulse of a spin echo acquisition. See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The inversion recovery sequence has the advantage, that it can provide very strong contrast between tissues having different T1 relaxation times or to suppress tissues like fluid or fat. But the disadvantage is, that the additional inversion radio frequency RF pulse makes this sequence less time efficient than the other pulse sequences.

Contrast values:
PD weighted: TE: 10-20 ms, TR: 2000 ms, TI: 1800 ms
T1 weighted: TE: 10-20 ms, TR: 2000 ms, TI: 400-800 ms
T2 weighted: TE: 70 ms, TR: 2000 ms, TI: 400-800 ms

See also Inversion Recovery, Short T1 Inversion Recovery, Fluid Attenuation Inversion Recovery, and Acronyms for 'Inversion Recovery Sequence' from different manufacturers.