Acceleration of energetic charged charged particles, most-often with power-law energy spectra occurs everywhere is space where particle-particle collision mean free paths are significantly larger than their gyro-radii. Shocks, reconnection events and turbulence have variously been proposed as acceleration mechanisms, and each must currently be considered a viable mechanism. Shocks have the advantage that they produce naturally power-law spectra in the observed range which are not very sensitive to the parameters. They are usually also fast accelerators. I first discuss the constraints which observations place on the acceleration mechanisms and show that there are both temporal and spatial constraints. Stochastic acceleration tends to be slow, so the rate of acceleration is important. In the inner heliosphere, this rate must exceed the rate of adiabatic cooling ≈ 2V w/r, where V w is the radial solar-wind velocity. Acceleration of anomalous cosmic rays (ACR) in the heliosheath must occur on a time scale of on year to avoid producing too many multiply charged ACR. It is shown that here, stochastic acceleration has difficulties in the inner heliosheath. Reconnection events are essentially incompressible, so the divergence of the flow velocity is nearly zero, and the Parker equation would give little acceleration. Acceleration at reconnection therefore must go beyond the Parker equation-either by invoking large pitch-angle anisotropies or by extending the equation to higher order in the flow speed relative to the particle speed. An approach to using an extension of Parker's equation is discussed. Diffusive shock acceleration at the heliospheric termination shock is also discussed. It is suggested that inclusion of upstream turbulence and shock geometry provides reasonable solutions to the perceived problems with this mechanism. Finally, observation evidence is presented which suggests, strongly, that the acceleration of the ACR occurs in the inner heliosphere, not far from the heliospheric termination shock.