Normally I answer this stuff on the forum, but this one made it in an email. Reposting here, in case anyone else someday has this question....

I am confused about the reference card that came with the Teensy 3.1: There is a statement on the card that says a 150 uFd cap should be added. .......
In an ideal world, where I could get an infinite amount of hardware and software development done, Teensy 3.1 would have USB host capability. It may yet someday, but it'll be at least a year until I even touch it, and it's a huge software project, so odds are slim it'll happen anytime soon.

But in that scenario, a USB host is supposed to have at least 120 uF capacitance. USB device are supposed to have under 10 uF. These are requirements you can find in the official USB spec. The idea is for hot-plugging, the charge is shared between the already charged 120 uF and not-yet-charged 10 uF. The 120 uF min on the host and 10 uF max on the device is meant to prevent a hot-plug connection from draining the host's power below 4.5V while charging the device's capacitor.

On Teensy 3.1, the optional capacitor is meant to allow you to meet that 120 uF min, so Teensy's power supply won't get pulled too low during a hot-plug event. Obviously you do NOT want to add that if using Teensy as a device, since it could cause Teensy to put too much load on your PC during a hot plug event.

As for where it's connected, please refer to this schematic:

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The USB host shield is not a PJRC product, so anything I say in this message should be trumped by real info from Circuits@home.

The basic idea, that hosts need over 120 uF and devices need to be no more than 10 uF is part of the USB spec. I'm not familiar with what the host shield does to meet that USB requirement, or if it's even designed to do so. But it really should have something, since a USB device can be hot plugged. Ideally, the host shield should handle hot plugging of devices, so in theory Teensy shouldn't need to have that capacitor added, since the host shield is providing the USB host capability. (but in practice, many products in the Arduino market aren't always really well designed...)

I'm not sure if this lengthy message really answered your question, and I'm a bit reluctant to make specific recommendations for a non-PJRC product. But hopefully this gives you a solid idea of why Teensy 3.1 has the spot to add a big capacitor.