House Committee on Rules

The Rules Committee has two broad categories of jurisdiction: special orders for the consideration of legislation (known as “special rules” or “rules”) and original jurisdiction matters. A special rule provides the terms and conditions of debate on a measure or matter, consideration of which constitutes the bulk of the work of the Rules Committee. The Committee also considers original jurisdiction measures, which commonly represent changes to the standing rules of the House, or measures that contain special rules, such as the expedited procedures in trade legislation. (source)

http://rules.house.gov/

Chair:
Rep. Pete Sessions [R-TX32]
Ranking Member:
Rep. Louise Slaughter [D-NY25]
Republicans:
9
Democrats:
4

The chair is always selected from the majority party and the ranking member is the most senior member of the minority party. The majority party ensures it has a majority on every committee.

Chair
Pete Sessions
TX-32
Republican
Ranking Member
Louise Slaughter
NY-25
Democrat
Ranking Member, Subcommittee on Rules and Organization of the House
Rules ...
Doug Collins
GA-9
Republican
Legislative ...
Rob Woodall
GA-7
Republican
Chair, Subcommittee on Legislative and Budget Process
Legislative ...
Alcee Hastings
FL-20
Democrat
Ranking Member, Subcommittee on Legislative and Budget Process
Ken Buck
CO-4
Republican
Michael Burgess
TX-26
Republican
Bradley Byrne
AL-1
Republican
Liz Cheney
Wyoming
Republican
Tom Cole
OK-4
Republican
James “Jim” McGovern
MA-2
Democrat
Dan Newhouse
WA-4
Republican
Jared Polis
CO-2
Democrat

There are 129 bills referred to this committee. Below find the top 100: