All Nippon Airways (ANA) has reduced fuel surcharges drastically on awards that travel to or from Japan. Now you can fly to Tokyo from the United States for 75,000 miles in flat bed Business Class roundtrip plus low taxes plus a $4--yes four dollar--fuel surcharge. That's tens of thousands of miles fewer than competitors charge.

The above screenshot is of a roundtrip Business Class award flying ANA between Los Angeles and Tokyo in February 2017.
Routing Rules
ANA has two award charts.

Today (May 11, 2016) is the last day to take advantage of the 30% discount on Virgin Atlantic economy awards that brings the price of an award between select U.S cities and London down to only 12,250 Virgin Atlantic miles and $134.60 in taxes and fuel surcharges.

If you stack that Virgin Atlantic economy sale with the current deal American Express is offering-- a 30% transfer bonus of Membership Rewards to Virgin Atlantic through May 31, 2016--then you can book an award to London for only 10,000 Membership Rewards +$134.60!! Book now, but not as a roundtrip.
Why

The current public sign-up bonus offers for the Cit AAdvantage Platinum Select Mastercard, CitiBusiness AAdvantage Platinum Select Mastercard, and the Citi ThankYou Premier Mastercard are 30k, 30k, and 0 (no bonus) respectively.

But you can do much better.

The following links have surfaced with much higher sign-up bonus offers:

Citi® / AAdvantage® Platinum Select® World MasterCard®
CitiBusiness® / AAdvantage® Platinum Select® World MasterCard®
Citi ThankYou® Premier MasterCard®

Citi® / AAdvantage® Platinum Select® World MasterCard®

This card's public sign-up offer is 30,000 American Airlines miles for spending $1,000 within three months of opening the account.

Book any JetBlue award by 11:59 PM EST TODAY (May 10, 2016) for travel from now to June 30, 2016, and you’ll get 15% of the points back a month to six weeks after your flight.

JetBlue's loyalty program is revenue based, meaning the number of points you need is based on the ticket price. JetBlue points are worth roughly 1.5 cents each toward a ticket. Read this post to learn the basics about JetBlue awards.

The highest value award is for Mint Class between New York and Los Angeles and New York and San Francisco.

A few years ago, I created a manual for award booking. I thought the best way to organize it was to explain the key concepts of all awards in the beginning, and then explain each major program in detail afterwards. Here is the first section of the manual--nine key concepts of all award bookings. I've edited it slightly today to make sure it is up to date.

Are there any other key concepts you would add to a manual of award booking?
Key Concept 1
Each type of miles has its own rules.

You can earn 700 AAdvantage miles by entering American Airlines' Miles for Milestones giveaway, a celebration of the 35th anniversary of the American Airlines AAdvantage® program. 35 winners will be chosen for the grand prize of 350,000 AAdvantage miles.                                                           _

Getting approximately $12 worth of miles for about five minutes of work is a great deal for me, especially since it resets the expiration clock in your American Airlines account, extending your entire mileage balance's expiration for 18 months.
What to Do
1.

Regarding any information in this post about taxes: this is miles information, not tax advice. Consult a tax professional before paying your taxes with a credit card.

Plastiq is an online bill payment processing system that "empowers you to use your existing debit and credit cards to pay any bill, regardless of acceptance". The charge for that convenience is 2.5% of each payment on a credit card and 1% on a debit card.

Last week my friend flew 24 hours of Lufthansa First Class and had a 3.5 hour layover in the famous Lufthansa First Class Terminal, which he booked for 125,000 United miles and $58.

Elite members of United’s MileagePlus frequent flyer program get access to extra Saver award seats in economy class. (Platinum and higher members also get extra business and first class seat availability.)

United credit card holders also get the extra Saver economy award space set aside for elites. That includes people with the United Explorer, Business Explorer, and Club cards.

I consider this one of the biggest benefits of the cards, and, oddly, it is a benefit that is completely unadvertised and possibly unintentional.
Recent Example
I have the United Business Explorer card and no elite status with United.

It seems that experflyer.com is not accurately displaying Air Tahiti Nui award space that Delta agents can book. Multiple Delta representatives confirmed with me over the phone that four seats in Business Class are available on seven different Air Tahiti Nui flights, all of which show zero award seats in Business Class available on expertflyer.com.
What Air Tahiti Nui Is and Why it Matters
Air Tahiti Nui, headquartered in Papeete, Tahiti, is one of seven airlines that flies into Fa'a'ā International Airport in Tahiti.