Combine:
an alien race comprised of multipule races which are combined through generations of superior technological and biological conditioning. the Combine is more like a coalition of aliens, rather than any one alien.
the orginal (presumed) combine is commonly seen in files as 'the Advisor' large slug like beasts which can be seen in Half-Life 2: EP. 1 and 2, first in a pod during your escape from the citidel and second during the farm house sequence. these slugs have increadably powerful Psyionic capabilities but have physically grown to massive bloated flesh bags.
other than the orginals, combine are seperated into other sub-catagories.
Synths and Troops
Synths are massive beasts of probably the first race enslaved by the combine. although possibly orginally something that could of ressembled humans, several thousand years of medical and scientific manipulation has reformed this entire race into massive living war-machines which is a fusion of technology and biology. these are your stryders, dropships, and gunships which each look more like large beasts with weapons and tech melded right into their bodies.
Troops are the average foot slogging beasts used as a bulk of the ground force by the combine during their invasion. the combine force that invades the earth are not acctually seen in the orginal Half life but are shown in the expansion 'Opposing Forces' as 'alien X' that act as the primary opposition to the Marine player and his Squad of assorted people. The troops are usually freshly conqured races which have had very minimal interaction with combine tech save for a few biological enhancements.
on earth, the Humans encountered which are called 'combine' are humans which have undergone biological enhancement fusing their body with technological bits and peices. these are split between 3 factions.
Civil protection (canidates/police force/un-augmented)
Soldiers (modertly augmented)
Elite (Heavily augmented and canidites to be put into combine service)
travel.
the combines main source of teleportation technology is dependent on simply generating a massive amount of power and tearing a hole between point a and b. because they have the resources to do this, they never looked for an alternative to this method of teleportation. however when they are teleported to less technologically advanced worlds which lack the facilities and resources to construct or generate the power supply required (like earth) they have to depend on local transportation methods to get around.
Breen.
Breen was put in power after negotiating the surrender of the human race after 7 hours. during this time, most all major super powers where heavily destroyed. mostly because they where caught off guard fighting an enemy which could instantly reinforce anywhere (because of the resonince cascade created by the HL1 experiment). for the most part, breen is used as a puppet for the combine, as a human face for the alien overlords.
why the resistance was able to win.
until a world builds its first teleportation platform (presumably what the numbered cities where doing, slowly recycling the resource of an entire city to construct this combine platform, they are cut off from the rest of the combine save for communication.
the only reason they where capable of getting to earth in the first place was because of the warp storm which made earth a giant beacon for teleportation. presumably they where doing this for a limited period of time before the warp storm was stopped (with the addition of hunters which where never seen before the episode and the massive convoy of troops and synths seen on the bridge.