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Several yaku requires that the hand is concealed. A concealed hand can be won on a discard. If the discarded winning tile finishes a pung, the pung is considered open when scoring the minipoints, but the hand as such is still concealed.
The yaku are all cumulative, so several yaku may be combined in the same mahjong hand. E.g. a concealed hand with All Simples and Mixed Triple Chows is worth 4 yaku on a self-draw. If the hand is open, it is worth only one yaku. No more than thirteen fan can be obtained in this way.
Yakuman are not cumulative.

Riichi riichi Concealed waiting hand declared at 1000 points stake. See 3.3.12 for the detailed rules of declaring riichi. An extra yaku, ippatsu, is awarded for winning within the first un-interrupted set of turns after declaring riichi, including the next draw by the riichi declarer. If the set of turns is interrupted by claims for kong, pung or chow, including concealed kongs, the chance for ippatsu is gone.
An extra yaku, daburu riichi, is awarded for declaring riichi in the first set of turns of the hand, i.e. in the player’s very first turn. The first set of turns must be uninterrupted, i.e. if any claims for kong, pung or chow, including concealed kongs, has occurred before the riichi declaration, daburu riichi is not possible.

Fully Concealed Hand menzen tsumo Winning on a self-draw on a concealed hand.

All Simples tanyao chuu Concealed hand with no terminals and honours.

Pinfu pinfu Concealed all chows hand with a valueless pair. I.e. a concealed hand with four chows and a pair that is neither dragons, nor seat wind, nor prevailing wind. The winning tile is required to finish a chow with a two-sided wait. The hand is by definition worth no minipoints, only the base 30 on a discard or 20 on self-draw.

Pure Double Chow iipeikou Concealed hand with two completely identical chows, i.e. the same values in the same suit, e.g.:
 

Mixed Triple Chow san shoku doujun Hand with three chows of the same numerical sequence, one in each suit, e.g.:
  
Gives an extra fan if concealed.

Pure Straight itsu Hand with three consecutive chows in the same suit, e.g.:
  
Gives an extra fan if concealed.

Dragon Pung fanpai/yakuhai Pung/kong of dragons.

Seat Wind fanpai/yakuhai Pung/kong in player’s seat wind.

Prevailing Wind fanpai/yakuhai Pung/kong in the prevailing wind.

Outside Hand chanta All sets contain terminals or honours, and the pair is terminals or honours. The hand contains at least one chow. Gives an extra fan if concealed.

After a kong rinshan kaihou Winning on a replacement tile after declaring a kong. Counts as self-draw.

Robbing the kong chan kan Winning on a tile that an opponent adds to a melded pung in order to make a kong, see Section 3.3.7. Since the kong is not declared successfully, no kan dora is revealed. Counts as ron (win on a discard). Robbing the kong also applies when winning on Thirteens Orphans on a tile used by an opponent for making a concealed kong. Only in the case of Thirteen Orphans can a concealed kong be robbed.

Under the Sea haitei Winning on self-draw on the last tile in the wall.

Under the Sea houtei Winning on the discard after the last tile in the wall. (This discard can only be claimed for winning, not for kong, pung or chow).

Seven pairs chi toitsu Concealed hand with seven different pairs. Two identical pairs are not allowed. Seven Pairs always scores exactly 25 minipoints; extra minipoints for e.g. a pair of dragons is not awarded.

Triple Pung san shoku dokou Hand with three pungs/kongs, one in each suit, of the same number, e.g.:
  

Three Concealed Pungs san ankou Hand with three concealed pungs/kongs. Note, the entire hand is not required to be concealed.

Three Kongs san kan tsu Hand with three kongs.

All Pungs toi-toi hou Hand with four pungs/kongs and a pair.

Half Flush honitsu Hand with tiles from only one of the three suits, in combination with honours. Gives an extra fan if concealed.

Little Three Dragons shou sangen Hand with two dragon pungs/kongs and a pair of dragons. Add the two yaku for the individual dragon pungs.

All Terminals and Honours honroutou Hand containing only terminals and honours. Add two yaku for All Pungs (toi-toi hou) or Seven Pairs (chi toitsu).

Terminals in All Sets junchan All sets contain terminals, and the pair is terminals. The hand contains at least one chow. Gives an extra fan if concealed.

Twice Pure Double Chows ryan peikou Concealed hand with four chows which two and two form Pure Double Chows, e.g.:
   
No additional yaku for Pure Double Chow (iipeiikou) are counted.

Full Flush chinitsu Hand composed entirely of tiles from only one of the three suits. No honours allowed. Gives an extra fan if concealed.

All Terminals and Honours Discard nagashi mangan This special hand cannot be combined with any other hand. After an exhaustive draw, a player can claim this special hand if he has a concealed hand, has discarded only terminal and honour tiles and none of his discards has been claimed. The player does not have to be tenpai. The player receives payment equivalent to a self-drawn mangan, plus counters and riichi bets.

Thirteen Orphans kokushi musou Concealed hand with one of each of the 13 different terminal and honour tiles plus one extra terminal or honour tile, e.g.:
 

Nine Gates chuuren pooto Concealed hand consisting of the tiles 1112345678999 in the same suit plus any one extra tile in the same suit, e.g.:
 

Blessing of Heaven tenho East winning on his initial deal. Concealed kong is not allowed.

Blessing of Earth chiho Winning on self-draw in the very first un-interrupted set of turns.
Concealed kong is not allowed.

Blessing of Man renho Winning on a discard in the very first un-interrupted set of turns, before the player has had his first turn. Concealed kongs are also considered to interrupt the set of turns.

Four Concealed Pungs suu ankou Concealed hand with four concealed pungs/kongs.
Winning on a discard is allowed only in case of single wait on the pair.

Four kongs suu kan tsu Hand with four kongs.

All Green ryuu iisou Hand composed entirely of green tiles. Green tiles are: green dragons and 2, 3, 4, 6 and 8 of bamboo. E.g.:
    

All Terminals chinrouto Hand composed entirely of terminal tiles.

All Honours tsuu iisou Hand composed entirely of honour tiles.

Big Three Dragons dai sangen Hand with three pungs/kongs of dragons. In case of three melded dragon pungs/kongs, the player feeding the third set of dragons must pay for the entire hand in case of self-draw, and split the payment with the discarder in case of win on a discard. See section 3.3.6.

Little Four Winds shou suushii Hand with three pungs/kongs of winds and a pair of winds.

Big Four Winds dai suushii Hand with four pungs/kongs of winds. This hand is rewarded double yakuman payment. In case of four melded wind pungs/kongs, the player feeding the fourth set of winds must pay for the entire hand in case of self-draw, and split the payment with the discarder in case of win on a discard. See section 3.3.6.