I should begin by explaining that d20 Rethought basically uses the skills system from the Saga edition of the Star Wars Roleplaying Game. Your base skill bonus equals half your character level, +5 if you've selected it as one of your "trained" skills. Also, taking a page from the Spycraft rpg, all skills have critical success and error ranges, the exact results of which vary from skill to skill.
Now keeping that in mind: As a part of this overhaul, all combat-related rolls are skill checks. Grapple is a skill, trip is a skill. . .attack checks are made using the appropriate (Weapon Group) skill, meaning that proficiency in a weapon is gained by taking the relevant skill. Hit the link for a full list of combat-related skills and their applications.
-Block (Brawn): A move action lets you use the result of your block check in favor of your Guard defense against a single opponent.
-Parry (Grace): Similar to block, but better when using a weapon to guard against grace-based attack checks (which is the default for this system).
-Disarm (Brawn): Used on grappled opponents to take an item away.
-Pin (Brawn): Used in a grapple to immobilize and/or silence the opponent.
-Seize (Grace): .Used to initiate a grapple.
-Bull Rush (Brawn): As in 3.5.
-Overrun (Brawn): As in 3.5.
-Stagger (Brawn): Standard action. A staggered opponent takes a -4 penalty on combat skill checks and falls prone if they would become staggered again.
-Sweep (Strength): As in 3.5 with trip attempts.
-Throw (Strength): Like above, but used in close quarters (opponent's square) and can move an opponent.
Weapon Group 
-Attack (Grace): This is d20 rethought's attack roll.
And just to fill in a couple gaps, here are a few things feats will let you do:
-Disarm an opponent using your weapon.
-Use brawn instead of grace on attack checks with two-handed weapons and light mass weapons (an inverse Weapon Finesse since the default attack stat is ).
-Make a Stagger check as a move action.