Neutron generators are the source of neutrons for various applications. The different methods offer advantages and disadvantages in volume and energy of neutrons, portability, service life, and other factors.
Neutron generation from radioisotopes
Many radioisotopes continuously emit neutrons. This can be advantageous, when neutrons are desired, or a problem if one isotope of an element emits neutrons that are not needed in an application. A transuranic element, Californium's 252Cf isotope is widely used as a portable source for analysis. 
Plutonium has isotopes that both capture and emit neutrons. 239Pu is the neutron acceptor in nuclear weapons, but 240Pu, a neutron emitter, can cause predetonation; bomb-grade plutonium is not only 239-rich but 240-low. 240Pu, however, is beneficial in power reactors.
In the first nuclear weapons, an initiator, at the center of the fissionable material, emitted neutrons. Codenamed the "Urchin", it was a sphere of mixed polonium (210Po) and beryllium.  Without going through its complex mechanical design, the basic material was a hollow beryllium sphere, grooved on the inside, and with a solid beryllium pellet at the center. As the urchin was explosively compressed and vaporized, alpha particles emitted by the Po-210 then struck beryllium atoms, which released neutrons. The bomb also depended on a number of other mechanical aids to generate enough neutrons for the critical mass, such as neutron-reflecting outer shells that redirected neutrons into the core
Neutron generation from particle accelerators
Later neutron sources, based on linear particle accelerators, which is a cylinder with an ion source at one end and an ion target at the other end. The space between them contains deuterium, tritium, or some mixture depending on the specific generator design. Electrical current supplied to the source causes an electrical arc and generates hydrogen ions, which are then accelerate using electromagnetic force from another, accelerating electrode, which sends the accelerated cloud into the target. Individual neutrons (i.e., not a beam) are generated by the ions hitting the target, which has one or more hydrogen isotopes on its surface. 
The most obvious difference between the unclassified generators used in industry, and the classified detectors used in weapons, is size and ruggedness. Both types do have a superficial resemblance to a household hair dryer, with the ion source at the motor/heater end. The first tube used titanium hydride targets, but the standard in the indusctry uses scandium hydride.
One unclassified design described by Sublette is the Milli-Second Pulse (MSP) tube developed at Sandia. "It has a scandium tritide target, containing 7 curies of tritium as 5.85 mg of ScT2 deposited on a 9.9 cm2 molybdenum backing. A 0.19-0.25 amp deuteron beam current produces about 4-5 x 107 neutrons/amp-microsecond in a 1.2 millisecond pulse with accelerator voltages of 130-150 KeV for a total of 1.2 x 1010 neutrons per pulse. For comparison the classified Sandia model TC-655, which was developed for nuclear weapons, produced a nominal 3 x 109 neutron pulse." The neutrons are not produced as a burst, as a stream that triggers successive neutron multiplication cycles in the ultimate target. In the design of an ENI, the critical parameters are the beam intensity, and the speed and shape of the initial ionization pulse.
In a weapon, the ENI can be placed wherever mechanically convenient, as long as it is within 1-2 meters of the core and not separated by a neuttron absorber. Since the neutron generator usually contains tritium, radioactive decay of the tritium means that the generators are components that need periodic replacement. 
New, more compact and long-lived ENIs are available. Obviously, an ENI for a bomb does not need a long service life once active, but industrial generators have tended to exhaust their ions. New generator designs, however, provide the target with a source of fresh ions. The lifetime of these new devices may be in the thousands of hours. 
Neutron generation from nuclear reactors
While nuclear reactors are the least portable source of neutrons, they also can be the most powerful, and offer a range of neutron characteristics that are especially useful in analysis. By using different reactors, different placement of targets with respect to the reactior, and the moderators used in the reactor, the widest possible range of neutron fluxes can be obtained. The flux distributions contain thermal, epithermal, and fast neutrons. 
- Contemporary Physics Education Project (CPEP) (2003), Chapter 13 “... but What is it Good for?”, Nuclear Science—A Guide to the Nuclear Science Wall Chart, Lawrence Berkeley Laboratory, at 13-1
- Carey Sublette (Version 2.18: 3 July 2007), Section 8.0 The First Nuclear Weapons, Nuclear Weapons Frequently Asked Questions
- Sublette, Carey (Version 2.18: 3 July 2007), 184.108.40.206 External Neutron Initiators (ENIs), Nuclear Weapons Frequently Asked Questions
- Burroughs, Chris (January 28, 2000), "Researchers model neutron generator in hostile radiation environment: Reentry vehicle radiation transport simulated in 3-D for first time", Sandia Labs News (no. 2)
- Technology Transfer, Lawrence Berkeley Laboratories, Compact Neutron Generators, IB-1764
- Worcester Polytechnic Institute's Nuclear Engineering, Neutron Activation Analysis