What types of subject matter are statutorily eligible/ineligible for patent protection?

Section 101 of the Patent Act (35 U.S.C. 101) specifies four broad categories of patent eligible subject matter:

-processes
-machines
-manufactures (or articles of manufacture)
-compositions of matter
-any new and useful improvement of any the above

Case law has specified three broad categories of statutorily ineligible subject matter:

-abstract ideas
-laws of nature
-natural phenomenon