If I understand the Unicode spec properly, there's an important distinction between Unicode code points (what we tend to think of as characters) and Unicode encodings, e.g. UTF-8. The current version of Unicode defines "only" 0x10FFFF code points or possible characters, which they claim should be more than enough to handle every character in every modern and historical language every written.

There are then a variety of transformation formats defined for representing Unicode code points as actual bytes/octets:

• UTF-8: a variable-length encoding in which Unicode code points 0-127 (also ASCII chars 1-127) are represented by a single octet, and other code points are represented using from 2 to 6 octets. Used by Perl internally and also intended for places like HTML documents where reducing file size and transmission time for the common case is particularly desriable.
• UTF-16: a two-octet encoding that can represent about 63K Unicode codepoints, including large numbers of the CJK (Chinese-Japanese-Korean) unified ideograms. Some octet values in UTF-16 are reserved for surrogate pairs, in which two sequential codepoints represent one of the codepoints larger than 0xFFFF.
• UTF-32: a four-octet encoding scheme that represents every Unicode codepoint without any form of escaping or surrogates. This does not, however, mean that there are actually 2^32 possible Unicode codepoints -- despite having 32 bits to work with, UTF-32 values larger than 0x10FFFF are explicitly illegal. (See here.)