US Code Title 47, Section 227
The official copy of 227 (this is really slow)

47 U.S.C. § 227(a)(4) 
The term ''unsolicited advertisement'' means any material advertising the commercial availability or quality of any property, goods, or services which is transmitted to any person without that person's prior express invitation or permission.

47 U.S.C. § 227(b)(1)(C) 
It shall be unlawful for any person within the United States to use any telephone facsimile machine, computer, or other device to send an unsolicited advertisement to a telephone facsimile machine;

47 U.S.C. § 227(b)(3).
A person or entity may, if otherwise permitted by the laws or rules of court of a State, bring in an appropriate court of that State -
(A) an action based on a violation of this subsection or the regulations prescribed under this subsection to enjoin such violation,
(B) an action to recover for actual monetary loss from such a violation, or to receive $500 in damages for each such violation, whichever is greater, or
(C) both such actions.

If the court finds that the defendant willfully or knowingly violated this subsection or the regulations prescribed under this subsection, the court may, in its discretion, increase the amount of the award to an amount equal to not more than 3 times the amount available under subparagraph (B) of this paragraph.

47 U.S.C. § 227(d)(1)(B) 
It shall be unlawful for any person within the United States to use a computer or other electronic device to send any message via a telephone facsimile machine unless such person clearly marks, in a margin at the top or bottom of each transmitted page of the message or on the first page of the transmission, the date and time it is sent and an identification of the business, other entity, or individual sending the message and the telephone number of the sending machine or of such business, other entity, or individual.

Note: fax.com has been notified many times by the FCC so treble damages of $1,500 apply. They have violated both 47 U.S.C. § 227(b)(1)(C)  and 47 U.S.C. § 227(d)(1)(B) because they do not identify the business and telephone number of the business that they are sending the fax on behalf of.

Broadcast Fax and Junk Email Illegal Under 47 U.S. Code 227  
Has excerpts on both california and federal law showing the most often used sections related to junk faxes

United States Code 
The whole US Code (Cornell version)

US CODE--Electronic Edition 
The official US Code (from US government site)

Interpretation of federal law

FCC page on the TCPA
This has a summary of the FCC rulings clarifying the TCPA. This is an excellent resource. It clarifies that "the mere distribution or publication of a telephone facsimile number does not confer invitation or permission to transmit advertisements to a particular telephone facsimile machine" and that the sender of the fax refers to the client of a fax service. If the fax broadcaster wants to add their identification as well, that's fine, but the header must have the business name and telephone number that the broadcaster is sending the fax on behalf of.

FCC unsolicited fax orders (TCPA actions)
This page has a summary of citations sent out by the FCC in the past years. These citations summarize the law as well. Click on any of the citations available in both text format (the default) as well as in Word format (by clicking the link at the top of the page).

FCC citation of 21st Century Faxes
Here's one of the citations contained on the FCC unsolicited fax orders. Explains the law in more detail to violators. Mentions in particular, you can't just swipe a fax number you see somewhere and fax to it. Here's what they write in their typical citation:

Section 227(b)(1)(C) of the Act prohibits any person from using “a telephone facsimile machine, computer, or other device to send an unsolicited advertisement to a telephone facsimile machine.”18 An unsolicited advertisement is defined as “any material advertising the commercial availability or quality of any property, goods, or services which is transmitted to any person without that person’s prior express invitation or permission.”19 The Commission has determined, however, that an established business relationship demonstrates consent to receive telephone facsimile advertisement transmissions.20 The mere distribution or publication of a telephone facsimile number does not confer invitation or permission to transmit advertisements to a particular telephone facsimile machine.21

FCC forfeiture letter against 21st Century
The FCC came out with a final determination against 21st Century Faxes and determined that TCPA applies even if you are faxing from outside the US. The FCC said:

Accordingly, we conclude that the TCPA prohibits the faxing of unsolicited advertisements either to or from the United States by any entity that is located ``within the United States.'' Moreover, the term ``person'' in Section 227(b)(1) includes the individual who actually performs the faxing as well as the corporate entity on whose behalf he or she is acting.16

and ruled that 21st Century has sufficient US presence to qualify as "being within the US." They noted that:

47 U.S.C. § 227(b)(3), Congress focused
on the violator having a presence in the United States such
that the state courts would have personal jurisdiction.

AND

Moreover, the term ``person''
in Section 227(b)(1) includes the individual who actually
performs the faxing as well as the corporate entity on whose
behalf he or she is acting.16

Plaintiffs are Limited to Exclusive State Court Jurisdiction 
Discusses "opt-in" and "opt-out" aspects of the TCPA. Basically, no state has opted out and virtually all courts have allowed the cases. In Texas, a case was thrown out until the Texas

junkfaxes.org - Helping to Stop Illicit Junk Faxes
This site has lots of great resources, but it's got a flakey webserver and often unreachable.

Consumer News What You Can Do About Unsolicited Telephone Marketing Calls and Faxes
FCC page for consumers on junk faxes

Small Claims Court Enforcement of Federal Unsolicited Fax Law  
Suggestions from a lawyer on how to modify federal law regarding unsolicited faxes

Using Class Actions to Enforce Unsolicited Fax Law 
A 1998 article on why this wouldn't work in federal court. Gives reasons that class certification might be denied. Doesn't apply here in California as pointed out at the end.

Actions to Enforce Federal Unsolicited Fax Law 
A very old article about the TCPA and whether it is enforceable. My how times change. This was written in 1998.

Pre-recorded Telephone Calls; Unsolicited Fax & E-Mail Ads  
BBB interprets the federal and California law