How Does Bleaching Or Dyeing Affect The Hair?

Bleaching opens the cuticle/hairshaft of the hair and lifts out your natural color. Permanent dyes open the hairshaft, and "in the first 15 minutes of processing", lift your natural color about 2 shades, then deposits the haircolor in the next 15 minutes. Temporary colors only deposit the color onto the hairshaft without opening the cuticle.
Everyone who answered here made excellent points. Coloring hair for the first time is a snap. It is the succeeding processes that will damage your hair if not applied to the new growth only, then weakening the remainder of the leftover color with water to lower the volume of the developer to around 10%: Then applied to the hair which was previously processed, for color deposit only. And it should only be applied in the last 10 minutes of processing, just to freshen up the previous color application.
However, this is not the case when bleaching. Only the new growth should be bleached, being careful not to overlap with the previously bleached hair.
Hair can be grown as long as you want it be: Colored throughout the growing process, and still remain as healthy and shiny as ever as long as it is applied properly and with professional products.
O boy, I rattled on a bit again. Please excuse me for that.

Bleaching and coloring hair can damage hair shafts. These processes lift the scales on the hair shaft allowing needed oils and nutrients to escape. Some Colors are more damaging than others. One can keep a healthy head of hair by conditioning, conditioning, conditioning. Also it is helpful to time the processes apart, giving the hair time to restore, between damaging.

Bleach and dye can take the moisture out of the hair and cause it to break or become brittle. It leaves the hair feeling very course with too much dye or bleaching. Using conditioners made for bleached or dyed hair with help to restore the natural oils and moisture in the hair.

Dyeing your hair is not to bad for your hair if you don't do it to often but bleaching your hair is really bad for it as the chemicals are stronger and most of the chemicals are worse than the ones in hair dye also if you are bleaching your hair and it goes wrong then you have a more high chance of your hair falling out than if your using hair dye! But hair dye will still damage your hair.

Bleaching and dyeing, unless done properly and with good quality conditioners/bleaches/dyes, can strip the hair of it's natural oils, and make is more susceptible to damage. It also makes the hair brittle, and over time, it will fall out quickly.

I have tried it myself and had it done professionally, if your hair is fine and dark brown like mine is naturally, I can say from experience that it turns your hair very brittle, even when you use expensive conditioning products, and as others have said above the hair breaks, it literally snaps at weak points, and when wet it feels like stretchy rubber and you should never brush or comb it when it is wet. I liked the look but the damage is really dissapointing, I have lost so much hair from my salon blonde hair, and it is not peroxide blonde its more golden blonde because my hair was getting in such bad shape. It is going to take ages to regrow. I wouldn't reccomend it to dark haired people ever. Sadly though I love the idea of blonde hair, I am considering to go back to brunette and buy a blonde wig for fun instead!

Bleaching kills and stripes your hair of its color. Dye is like paint it bonds to the molecules and temporary changes there color

All bleaches and dyes used for hairs, contain not only the color but also many chemicals which make the tanning possible and also to stable the bleach and dye. The low grade raw material can destroy hair follicles and hair bulb which causes hair loss. For some peoples even a good quality raw material of bleach can cause allergy and cause hair loss and itchy patches on skin.

Can bleaching your hair make it go grey ? To settle an argument

It causes your hair to go dry without proper care and never dye the redye in the same day wait 24 to 48 hours before a new dye is used at all times

As Nidar said, it damages your hair if not done professionally. Your hair will look like straw.

What nidar has said is true. Bleaching and dying your hair will make it easier to damage. My mom has dyied her hair a lot and her hair has a lot of split ends and dead ends.

Yes bleaching your hair does make it brittle, and damaged and fall Out eventually.

Dose your hair stop growing if you bleach it ?

When you bleach or die your hair just once, it is usually fine, no harm done. But after a couple times your hair becomes weaker and it will eventually start to fall out!

Your hair will be damaged with both, bleach, and hair dye. No matter what, your hair WILL NOT fall out. But it does stripe your hair of it's natural oils, just make sure that you use the right types of conditioner and if you are doing it yourself think about asking your hair dresser what type of conditioner and shampoo can help strengthen your hair.