My training partner likes to say that past-failure techniques such as dropsets, cheat reps, partial reps, and even forced reps really only work because they give you a second chance at a high intensity set. Now this might sound like a bit of a philosophical viewpoint, but it's actually an ultra realistic one. Ultimately, intensity is the only deciding factor in growth and rate of growth. Yes, isolation plays a part as well, but your intensity level directly impacts how completely you exhaust each muscle, how often you train each muscle, it even determines the volume you use during your training.
As you approach failure, several factors may determine which technique, if any, you choose to use. Here are the most common past-failure techniques, along with a few guidelines and contraindications for each. Remember, use them one at a time!
1. Forced Reps
Forced reps, also called "spots," are one of the better choices for pushing past failure. This is because a spot is intended only to assist in pushing through sticking points in the strength curve, and not assist past that. Assistance should be given only on the concentric, and never on the eccentric. If you have to spot your partner on the way down too, he or she is training past their capacity. Forced reps are usually a fairly safe option because your spotter provides the necessary assistance for proper form maintenance. The "security net" provided by having a spotter is something that can and should be duplicated with safety bars whenever possible! Needing a partner is a major drawback to this method, and we all know it's not safe to ask random people at the gym!
2. Partial Reps
This is where partial reps come in. Rather than use the aid of an outside force, continue to perform reps up to the sticking point in the strength curve, maintaining form and explosivity to the greatest degree possible, even if you cannot complete the rep fully. Because you are not allowing your form to break down (aside from the intentional range of motion limitations), and because you are not relying on a spotter to complete reps, there really is no downside to partial reps. However, it is important to note that even during partial reps, completing the entire eccentric portion of the rep is very important! This means your "partials" will be at the "bottom" of the movement rather than the "top," i.e. starting from a stretch. Correct partials for dumbbell curls would be from rest (dumbbells at the side) up to the sticking point, whereas correct partials for squats would be from parallel; correct partials for pullups would be from a hanging stretch--not from the bar letting yourself part way down!
3. Cheat Reps
Here's the option most people use, and it's only because most people train way too heavy. Cheat reps are exactly what they sound like: a breakdown in form which allows other muscle groups to assist with the weight. But cheat reps can be performed in a limited manner that is conducive to growth. The most important thing to keep in mind when performing cheat reps is to maintain as much tension on the target muscle as possible--despite the assistance of other muscle groups. Cheat only as much as you absolutely need too; don't waste the effort you're putting into the set by making it too easy at the end! Obviously, cheat reps are not appropriate for every exercise, or even for every muscle group. Most lower body exercise are not cheat rep friendly because they require spine stability and precise execution. Some back and chest exercises do not mix well with cheat reps for the same reason: a need for stability of the spine and shoulder girdles, and a need for precise execution to avoid injury. Think logically about which muscles and joints can and do tolerate a degree of tension overlap, and which require a more precise application of overload.
4. Dropsets/Running the Rack
Dropsets, also called "running the rack," are an intensity increasing method where the working weight is decreased throughout the set, usually in equal increments, whenever failure is achieved. Dropsets can assist in a few ways: additional time under tension, additional explosive central nervous system training, additional tissue fatigue, and additional faschia stretching through sustained, increased bloodflow are all important facets of inducing hypertrophy. And by reducing weight at each sticking point, dropsets also facilitate proper form, which is an important facet of hypertrophy as well. Dropsets can also be used to add a little extra somethin' to sets where your rep range at the heaviest weight is a little too low.
For example, I approach failure with a set of eight or nine reps with 115 on front squats, but I feel like I need to hit my quads a little harder. But I can only do about four clean reps at 135 on front squats and that's too few for my training style. What's a girl to do? Instead of doing 135, and having my form most likely break down in order to reach the desired rep range, I do a drop set past my original working weight. So even though I may not get very many reps with that weight, I do get another chance at each lighter weight to push a little harder.