Super heavy-lift launch vehicles

Classification:

A small-lift launch vehicle is capable of lifting up to 2,000 kg (4,400 lb) to low Earth orbit.

A medium-lift launch vehicle is capable of lifting 2,000 to 20,000 kg (4,400 to 44,000 lb) of payload into low Earth orbit.

A heavy-lift launch vehicle is capable of lifting 20,000 to 50,000 kg (44,000 to 110,000 lb) of payload into low Earth orbit.

A super heavy-lift launch vehicle is a launch vehicle allowing to lift more than 50,000 kg (110,000 lb.) of payload into low Earth orbit. 

Retired or never used in operation:

Saturn V was an US super heavy-lift launch vehicle used by NASA between 1967 and 1973.  It consisted of three stages, each of them fueled by liquid propellants. It was developed for the Apollo program to the Moon and was later used to launch Skylab, the first American space station. Note: Saturn IB was used for the later Apollo-Soyuz test project.

Saturn V had with an Apollo program payload of a command module, service module, and Lunar Module a total mass of 45 t. When the third stage and Earth-orbit departure fuel was included, Saturn V actually had140 t into low Earth orbit. The final launch of Saturn V took Skylab,  with a 77,111 kg payload, into low Earth orbit.

The Apollo 11 Saturn V rocket launch vehicle, lift off at 9:32 a.m. EDT July 16, 1969, from Kennedy Space Center's Launch Complex Pad 39A.

The N1/L3 was a super heavy-lift launch vehicle which was supposed to deliver payloads beyond low Earth orbit. The N1 was the Soviet counterpart to the US Saturn V and was intended to enable crewed travel to Earth's Moon and beyond. N1 was developed in late 1960s and early 1970s and it made only 4 orbital launch attempts. After 4 failed attempts, the project was cancelled in 1976.

N1 on the launch pad at the Baikonur Cosmodrome in late 1967.

The Space Shuttle orbited a combined shuttle and cargo mass of 122,534 kg  when launching the Chandra X-ray Observatory on STS-93. Chandra and its two-stage Inertial Upper Stage booster rocket weighed 22,753 kg. 

Space Shuttle Columbia STS-93 launches in 1999

Energia was a super-heavy lift launch vehicle designed to launch up to 105 t to low Earth orbit. It was designed by NPO Energia of the Soviet Union for a variety of payloads including the Buran spacecraft. The Energia used four strap-on boosters each powered by a four-chamber RD-170 engine burning kerosene/LOX, and a central core stage with four single-chamber RD-0120 (11D122) engines fueled by liquid hydrogen/LOX. Energia launched twice before the program was cancelled, but only one flight reached orbit. On the first flight, launching the Polyus weapons platform (approximately 80 t), the vehicle failed to enter orbit due to a software error on the kick-stage. The second flight successfully launched the Buran orbiter.

In August 2016, plans were announced to develop a super heavy-lift launch vehicle from existing Energia components instead of the less-powerful Angara A5V project. 

Energia–Buran on launchpad before launch

In current operation:

Falcon Heavy is a partially reusable heavy-lift launch vehicle designed and built by SpaceX. It is derived from the Falcon 9 rocket and consists of a strengthened Falcon 9 first stage as the core with two additional Falcon 9-like first stages as strap-on boosters, which is similar to Evolved Expendable Launch Vehicle Delta IV Heavy launcher and proposals for the Atlas V Heavy and Russian Angara A5V. 

Falcon Heavy has ability to lift over 57 t. The Falcon Heavy vehicle has the highest payload capacity of any currently operating launch vehicle. It has the third highest capacity of any vehicle ever launched to the low Earth orbit, behind Saturn V and Energia.

They have successfully conducted 3 launches, with the first famous one on 6 February 2018, launching the Tesla Roadster with the dummy Starman. The second Falcon Heavy was launched on 11 April 2019, while all three booster rockets successfully returned to Earth. The third Falcon Heavy was launched on 25 June 2019. There are two scheduled launches on July 2012 and October 2021. There are more planned, but details come later. 

source: Wiki

Planned:

Long March 9 (Changzheng 9), a 140 000 kg to low Earth orbit capable rocket was proposed in 2018 by China, with plans to launch the rocket by 2028. Long March 9 is expected to carry a payload of 140 000kg into low Earth orbit, with a capacity of 50,000 kg to trans-lunar injection or 44,000 kg to Mars.

The Indian Space Research Organisation is conducting preliminary research for the development of a super heavy-lift launch vehicle which is planned to have a lifting capacity of over 50-60 t (mainly into low Earth orbit).

Yenisei RN STK-1, is the first super-heavy launch vehicle being developed by the Russian space agency since the fall of the USSR. The main developer is RSC Energia and was proposed by Russia's RSC Energia in August 2016. The final design for the rocket is expected to be by autumn 2021. The first launch is expected to happen in 2028 from the Vostochny cosmodrome. The Don launch vehicle RN STK-2 is based on Yenisei, is also being developed by adding additional stage. 

The first stage should consist of 6 blocks, each based on the first stage of the planned Irtysh / Soyuz-5 rocket with an RD-171MV engine. The second stage will consist of one block, matching the first stage of Soyuz-6 with an RD-180 engine. The upper stage should be KVTK. KVTK is rocket stage, containing an RD-0146D engine and is designed for use on Angara rockets. Accelerating braking unit should be Block DM, which is an upper stage used on Soviet and later Russian expendable launch systems, including the N1, Proton-K and Zenit. 

Flight tests of a super-heavy launch vehicle should occur in two stages from 2028 to 2035. This super-heavy rocket is supposed to be used in the Russian lunar program, since the carrying capacity of the Angara-A5V launch vehicle (37 500 kg to low Earth orbit) is insufficient for these purposes. 

credit: Anatoly Zak, RussianSpaceWeb.com

The Space Launch System (SLS) is a US Space Shuttle-derived super heavy-lift expendable launch vehicle, which has been under development by NASA in since the announcement in 2011. It replaced the Ares I, Ares V, and Jupiter planned launch vehicles, which all were left in the development phase.

The Space Launch System's core stage contains the Main Propulsion System (MPS) of the launch vehicle. It has four RS-25 rocket engines at its base. The core stage is very similar to the Space Shuttle external tank. 

Blocks 1 and 1B of the SLS are planned to use two five-segment Solid Rocket Boosters (SRBs). These new SRBs are derived from the four-segment Space Shuttle Solid Rocket Boosters, with the addition of a center booster segment, new avionics, and lighter insulation.

Block 2 will have special advanced boosters which will make Block 2 be able to carry 131,541 kg to low Earth orbit and 45,359 kg to trans lunar injection.

The upper stage the Interim Cryogenic Propulsion Stage which is based on the Delta Cryogenic Second Stage used on Delta IV family of rockets. It uses one RL10 engine made by Aerojet Rockedyne.

The Exploration Upper Stage (EUS) is powered by four RL10 engines that produce almost four times more thrust than the one RL10 engine that powers the ICPS. With the EUS, NASA can use either a Block 1B crew configuration to send Orion, astronauts, and payloads to deep space or use a Block 1B cargo configuration to send large cargoes to the Moon, Mars, or more distant destinations.

There are planned 3 launches on November 2021 in Block 1 configuration Block 1 crew with payload Artemis 1 (uncrewed test flight) (Orion and ESM), om August 2023 in configuration Block 1 crew with payload Artemis 2 (the first scheduled crewed mission) (Orion and ESM), and on October 2024 in configuration Block 1 crew with payload Artemis 3 (Orion and ESM).  

credit: NASA

Blue Origin has plans to build a larger rocket than their New Glenn currently under construction, termed New Armstrong.

credit: wiki

As last planned and in a huge progress I mention the SpaceX Starship. The Starship system is a proposed fully reusable, two stage to orbit super heavy‑lift launch vehicle under development as a private project. Starship is transportation system designed to carry both crew and cargo to Earth orbit, the Moon, Mars and beyond. 

The booster stage Super Heavy is expected to be 72 m long and 9 m in diameter with a gross liftoff mass of 3,680 t. It is constructed up to now of stainless steel tanks and structure, holding subcooled liquid methane and liquid oxygen (CH4/LOX) propellants, powered by ~28 Raptor rocket engines that will provide 72,000 kN total liftoff thrust, which is the highest number to be. 

source: Wiki, SpaceX sea-level Raptor at Hawthorne 

The Raptor engine is powered by subcooled liquid methane and subcooled liquid oxygen using a more efficient full flow staged combustion cycle, different from the simpler open-cycle gas generator system and LOX/kerosene propellants that current Merlin engines use.

Left: full-flow staged combustion, Right: Open cycle gas-generator
Source: Wiki

Full-flow staged combustion (FFSC) is a twin-shaft staged combustion cycle that uses both oxidizer-rich and fuel-rich pre-burners. The cycle allows full flow of both propellants through the turbines. The fuel turbopump is driven by the fuel-rich pre-burner, and the oxidizer turbopump is driven by the oxidizer-rich pre-burner.

Gas-generator rocket cycle is a power cycle of a bipropellant rocket engine. Some of the propellant is burned in a gas generator and the resulting hot gas is used to power the engine's pumps. The gas is then exhausted. Because something is like thrown away, this type of engine is also then known as open cycle.