Many others, myself included, have touted the 3500 calories = one pound calculation, which is the accepted general rule, but out of good faith, I am adding one big caveat. My guidance is based on recent findings published in the International Journal of Obesity (http://www.nature.com/ijo/journal/v32/n3/abs/0803720a.html).

The short of this new (2010) research teaches us that while 3500 calories to lose a pound has always been the rule of thumb, this figure stems from research which (incorrectly) assumed that all the weight lost would be adipose tissue (which would be ideal, of course).

So, first of all, yes one pound of FAT = 3500 calories.

Here's where the caveat comes in. Because lean body mass is lost along with body fat, researchers now know the 3500 calorie figure is, for many, an oversimplification. The amount of lean body mass you will lose is based on your initial body fat level and size of your daily calorie deficit. Lean people tend to lose more lean body mass and retain more fat. Obese/overweight individuals tend to lose more body fat and retain more lean tissue (this explains why obese people can tolerate extremely low calorie diets better than already lean people, and why lean folks (close to their goal weights) have a devil of a time losing the last few pounds and need to be extra aware that they need to avoid an ultra low calorie approach to losing those pounds). Very aggressive low calorie diets erode lean body mass to a greater degree than more conservative diets. Whether you are losing lean or fat, tells you what is the required energy deficit per unit of weight loss is for you.

The metabolizable energy in fat is different than the metabolizable eneregy in muscle tissue. A pound of muscle is not 3500 calories. A pound of muscle yields about 600 calories. If you lose lean body mass then you lose more weight than if you lose fat. If you create a 3500 calorie deficit in one week and you lose 100% body fat, you will lose one pound. BUT if you create a 3500 calorie weekly deficit and as a result of that deficit, lose 100% muscle, you would lose approximately 6 pounds of body weight (a very bad thing).

If you have a high initial body fat percentage, then you are going to lose more fat relative to lean, so you will need a larger deficit to lose the same amount of weight as compared to a lean person. That means that eating at a lower calorie level will work better for you than for a relatively lean individual.

Creating a calorie deficit once at the beginning of a diet (e.g., a 750 calorie deficit per day) and maintaining that same caloric intake for the duration of the diet and after major weight loss fails to account for how your body decreases energy expenditure with reduced body weight. Your dietary needs will change as you lose weight. As you get lighter, your daily caloric need will diminish as will your body's ability to tolerate a too low calorie intake (consequence? you'll begin to lose more lean and hang onto the fat, thereby getting lighter but "fatter").

Weight loss typically slows down over time for a prescribed constant diet (we call this a "plateau"). This is either due to the decreased metabolism mentioned above, or a relaxing of the diet compliance, or both (most of us can't stick to excessive calorie reductions for long). Progressive resistance training and adequate caloric intake can modify the proportion of weight lost from body fat vs lean tissue.

So ... should you throw out the old calorie formulas? Not necessarily. You can still use the standard calorie formulas to figure out how much you should eat, and you can use a 500-1000 calorie per day deficit (below maintenance) as a generic guideline to figure where to set your calories to lose one or two pounds per week respectively (at least on paper anyway).

Even better however, you could use this info to fine tune your caloric deficit using a percentage method and also base your deficit on your starting body fat level, to get a much more personalized and effective approach:
15-20% below maintenance calories = conservative deficit
20-25% below maintenance calories = moderate deficit
25-30% below maintenance calories = aggressive deficit
31-40% below maintenance calories = very aggressive deficit (risky)
50%+ below maintenance calories = semi starvation/starvation (potentially dangerous and unhealthy)

(Note: According to exercise physiologists Katch & Mcardle, the average female between the ages of 23 and 50 has a maintenance level of about 2000-2100 calories per day and the average male about 2700-2900 calories per day)

A conservative deficit of around 15-20% below maintenance is often appropriate, especially for non-obese individuals.

In a nutshell, Dr. Hall’s research tells us that there are big differences between lean and overweight people in how many calories they can or should cut. If you are obese/significantly overweight, dramatic deficits will still result in a high (and desirable) ratio of fat loss to lean loss. If you are lighter, then you must pay more attention to being sure your calorie consumption doesn't drop too low. Be aware of where you are on this curve, and adjust as you make progress toward your healthy weight and body composition goal.