Who is the current minority whip of the senate?

The Word "whip" is used figuratively in the sense of "driver, overseer". The whip's role is to ensure party discipline; that is, to make sure that party members vote in accordance with official party policy. They can offer inducements (such as promotions to important committees) or threaten punishments (such as removal from important committees or withdrawal of party funding for a reelection campaign) to party members who seem likely to vote otherwise.

Technically, a quorum must be present for the house to "do business", but it's policy in both houses to assume that a quorum is present unless a "call for quorum" is specifically requested; it's therefore possible for debate to continue even if some (or even most) of the members leave the chamber. Another of the whip's jobs is to "round up" his party's members and get them back into the chamber when it's time to vote.

The position has no official standing under the Constitution (it's strictly up to a party whether they want to have a whip or not), and was first established around 1900.

The "minority whip" is the whip for the minority party in that house of congress (it's quite possible, and in fact is often the case, that the Minority Whip in the House of Representatives and the Minority Whip in the Senate are members of different parties). Technically, there could potentially be several "Minority Whips", but in practice minor parties (i.e. those other than Democrats or Republicans, currently) generally don't bother, since they don't have enough members (it's rare for there to be even ONE member of a minor party in office, so he'd be his Party Leader and would also have to do the job of his Party Whip ... making sure that he was present for the vote, and threatening himself to get him to vote properly).

As of April 2014, there are no members of the House that are not either Republicans or Democrats (the Tea Party is basically an ideological position within the Republican party rather than an actual party in its own right), and only two Senators who are neither Republicans nor Democrats (officially both are independent and not members of any party; in practice they nearly always vote with the Democrats).