Each Rank has a set amount of XP which must be earned to level up. After leveling up, you will unlock that rank's Dog Tag. You may unlock a Specialization or Weapon too. You start out on rank 0, no real rank name, and basic weapons. The following list has the level, the rank name, the XP needed to rank up, and the total amount of XP needed.

Private First Class: 1,000 (1,000) XP 870 MCS
Private First Class 1 Star: 7,000 (8,000) XP SPRNT
Private First Class 2 Stars: 10,000 (18,000) XP - Woodland Pattern Camouflage
Private First Class 3 Stars: 11,000 (29,000) XP - G17C
Lance Corporal: 12,000 (41,000) XP AMMO
Lance Corporal 1 Star: 13,000 (54,000) XP - Ranger Camouflage
Lance Corporal 2 Stars: 13,000 (67,000) XP PP-2000
Lance Corporal 3 Stars: 14,000 (81,000) XP FLAK
Corporal: 15,000 (96,000) XP - Army Green Camouflage
Corporal 1 Star: 15,000 (111,000) XP M9 TACT.
Corporal 2 Stars: 19,000 (130,000) XP EXPL
Corporal 3 Stars: 20,000 (150,000) XP - Expeditionary Force Camouflage
Sergeant: 20,000 (170,000) XP - MP443 TACT.
Sergeant 1 Star: 20,000 (190,000) XP - COVR
Sergeant 2 Stars: 30,000 (220,000) XP - Paratrooper Camouflage
Sergeant 3 Stars: 30,000 (250,000) XP UMP-45
Staff Sergeant: XP - SUPR
Staff Sergeant 1 Star: XP
Staff Sergeant 2 Stars: XP - G17C SUPP.
Gunnery Sergeant: XP - FRAG
Gunnery Sergeant 1 Star: XP
Gunnery Sergeant 2 Star: XP - M1014
Master Sergeant: XP - SQD SPRNT
Master Sergeant 1 Star: XP
Master Sergeant 2 Stars: XP - M9 SUPP.
First Sergeant: XP - SQD AMMO
First Sergeant 1 Star: XP
First Sergeant 2 Stars: XP - MP 443 SUPP.
Master Gunnery Sergeant: XP - SQD FLAK
Master Gunnery Sergeant 1 Star: XP - G18
Master Gunnery Sergeant 2 Stars: XP - SQD EXPL
Sergeant Major: XP - PDW-R
Sergeant Major 1 Star: XP - SQD SUPR
Sergeant Major 2 Star: XP - SAIGA 12K
Warrant Officer One: XP - SQD COVR
Chief Warrant Officer Two: XP - .44 MAGNUM
Chief Warrant Officer Three: XP - SQD FRAG
Chief Warrant Officer Four: XP - DAO-12
Chief Warrant Officer Five: XP
Second Lieutenant: XP - P90
First Lieutenant: XP - G18 SUPP.
Captain: XP
Major: XP - USAS-12
Lt. Colonel: XP - .44 SCOPED
Colonel: XP - AS VAL

using a kit as you play will level it up, just like your rank. Level up your kit to unlock more kit exclusive weapons or gadgets. Battlefield 3 calls it a score, such as Assault Score, but it's the same type of XP. The only difference is it's being directed to a Kit.

The following lists show the amount of score you need for each unlock. Some weapons are only unlocked in Co-Op mode with a Co-Op Score (CS).

Assault Kit

0 AS - M16A3 (US) / AK-74M (RU)
4,000 (4,000) AS - Defibrillator
7,000 (11,000) AS - M320
11,000 (22,000) AS - M416
16,000 (38,000) AS - M26 MASS
22,000 (60,000) AS - AEK-971
29,000 (89,000) AS - M16A4
35,000 (124,000) AS - F2000
42,000 (166,000) AS - AN-94
54,000 (220,000) AS - M16A3 (RU) / AK-74M (US)
126,000 CS - KH2002
441,000 CS - G3A3
Engineer Kit

0 ES - M4A1 (US) / AKS-74U (RU)
3,000 (3,000) ES - FIM-92 Stinger and SA-18 IGLA
4,000 (7,000) ES - M15 AT Mine
7,000 (14,000) ES - SCAR-H
11,000 (25,000) ES - EOD Bot
15,000 (40,000) ES - M4
18,000 (58,000) ES - A-91
24,000 (82,000) ES - FGM-148 Javelin
28,000 (110,000) ES - G36C
35,000 (145,000) ES - M4A1 (RU) / AKS-74U (US)
(378,000) CS - SG553
Support Kit

0 SS - M27 IAR (US) / RPK-74M (RU)
4,000 (4,000) SS - C4 Explosives
7,000 (11,000) SS - M249
12,000 (23,000) SS - M18 Claymore
17,000 (40,000) SS - M224 Mortar
20,000 (60,000) SS - PKP Pecheneg
30,000 (90,000) SS - M240B
40,000 (130,000) SS - M60E4
40,000 (170,000) SS - M27 IAR (RU) / RPK-74M (US)
Recon Kit

0 RS - MK11 MOD 0 (US) / SVD (RU)
5,000 (5,000) RS - T-UGS
8,000 (13,000) RS - SV98
13,000 (26,000) RS - SOFLAM
19,000 (45,000) RS - MAV
26,000 (71,000) RS - SKS
33,000 (104,000) RS - M40A5
42,000 (146,000) RS - M98B
49,000 (195,000) RS - MK11 MOD 0 (RU) / SVD (US)
252,000 CS - M39 EMR
Co-Op Unlocks

63,000 (63,000) CS - MP412 REX
63,000 (126,000) CS - KH2002
63,000 (189,000) CS - MP7
63,000 (252,000) CS - M39 EMR
63,000 (315,000) CS - 93R
63,000 (378,000) CS - SG553
63,000 (441,000) CS - G3A3

Using a vehicle on Multiplayer will route your XP to Vehicle Score (VS). That Score will rank up that particular vehicle to unlock Vehicle Gadgets, Vehicles Upgrades, and Vehicle Weapons.

The following lists show the Vehicle Score you need to unlock the upgrade, the total amount of Vehicle Score, and the upgrade you unlock.

MBT

800 (800) VS - IR Smoke
2,100 VS - Coaxial LMG
4,400 VS - Autoloader
7,600 VS - Zoom Optics
12,000 VS - Maintenance
17,700 VS - Coaxial HMG
24,700 VS - Proximity Scan
33,200 VS - Guided Shell
43,200 VS - Thermal Optics
54,800 VS - Thermal Camo
68,100 VS - Canister Shell
83,200 VS - Reactive Armor
100,000 VS - CITV Station
IFV

800 (800) VS - IR Smoke
2,300 VS - ATGM Launcher
4,700 VS - Belt Speed
8,300 VS - Coaxial LMG
13,100 VS - Thermal Optics
19,200 VS - Proximity Scan
26,900 VS - Zoom Optics
36,000 VS - Maintenance
47,000 VS - APFSDS-T Shell
60,000 VS - Thermal Camo
74,000 VS - Guided Missile
90,000 VS - Reactive Armor
Mobile AA

400 (400) VS - IR Smoke
1,200 VS - Anti-Air Missile
2,500 VS - Belt Speed
4,400 VS - Zoom Optics
7,000 VS - Proximity Scan
10,000 VS - Thermal Optics
14,000 VS - Air Radar
19,000 VS - Maintenance
25,000 VS - Thermal Camo
32,000 VS - Reactive Armor
Attack Helicopters

300 (300) VS - IR Flares
800 VS - Heat Seekers
1,600 VS - Stealth
2,800 VS - Autoloader
4,400 VS - Zoom Optics
6,500 VS - Proximity Scan
9,000 VS - Air Radar
12,000 VS - Guided Missile
16,000 VS - Extinguisher
20,000 VS - Maintenance
25,000 VS - Thermal Optics
30,500 VS - Laser Painter
37,000 VS - Below Radar
44,000 VS - ECM Jammer
51,000 VS - Guided Rocket
60,000 VS - TV Missile
Scout Helicopters

400 (400) VS - IR Flares
1,200 VS - Heat Seekers
2,500 VS - Stealth
4,400 VS - Belt Speed
7,000 VS - Proximity Scan
10,000 VS - Air Radar
14,000 VS - Extinguisher
19,000 VS - Maintenance
25,000 VS - Guided Missile
32,000 VS - Below Radar
40,000 VS - Laser Painter
48,000 VS - ECM Jammer
Jets

300 (300) VS - IR Flares
700 VS - Heat Seekers
1,500 VS - Stealth
2,700 VS - Belt Speed
4,200 VS - Proximity Scan
6,200 VS - Rocket Pods
8,600 VS - Air Radar
11,600 VS - Extinguisher
15,000 VS - Below Radar
19,000 VS - Maintenance
24,000 VS - Guided Missile
29,000 VS - Beam Scanning
35,000 VS - ECM Jammer