An authoritative introduction to Treasury strips is given by the US Treasury and the explanation by the NYFRB includes corporate zeroes as well.
The reason that yield curves typically slope upwards can be seen by comparing T-bills and Treasury strips, both of which usually have the same face value, $10,000. One instrument promises to pay $10k in, say, one year and the other promises to pay $10k in 10 years. The difference between the face value and the current market trading price is the discount. If the current price of a ten-year instrument is $5k, then the yield-to-maturity is 7%/year.
Bills, Treasury Strips, and Corporate Zero Coupon Bonds have the common property of no interest payments -- the only payment promised to the creditor is a balloon -- the contracted face value due at the date of maturity. The entire yield, therefore, comes from capital appreciation. One can draw a smooth exponential curve from today's price to the face value for which the slope of the curve is the yield. If, as never happens in practice, the instrument appreciated each day, month, year ... at the same percent, that trading price would climb smoothly up the exponential curve.
If the quoted yield-to-maturity is the slope of this hypothetical
curve, then consider the implications of a change in the yield for
prices of instruments at different maturities. Some instruments are
due in one year, others five years, ten years etc. Assume they all
have the same face value and trade at the same yield, 5%. The 10 year
instrument trades at a price which is