Even moving at 10 miles a second, like the Voyager spacecraft launched in the 1970s, it would take around 80,000 years to reach Alpha Centauri -- which is 4.2 light years away.
If we want to explore anything in the wider galaxy, the challenges are enormous ... and we don't even know how to keep astronauts safe.
Building a ship that can travel at enormous speeds is vital but there's one rather large elephant occupying the bridge of our vessel.
The Earth's atmosphere and magnetic field protect us from lethal radiation from the sun. Without similar protection from the hostile space environment we are not going anywhere very far -- at least, not alive. Even the relatively short hop to Mars puts explorers at serious risk. NASA says a Mars voyager would receive a radiation dose around 100 times the average yearly exposure on Earth.
Cladding for a spacecraft would have to be meters thick to give full protection, and too heavy to be viable. Lining the spacecraft with water or even the astronauts' own waste have been suggested as possible solutions.
Perhaps there's another way. Scientists at the UK's Rutherford Appleton Laboratory (RAL)
have been working on an idea to protect space travelers, taking inspiration from the "Star Trek" shield.
The plan is to make a mini magnetosphere
-- a tiny version of the magnetic field that shields the Earth -- to protect people and spacecraft components.
"It's got to be solved," said Ruth Bamford, lead researcher for the deflector shield project at RAL, telling CNN that the problem was a "potential show stopper for manned exploration."
As a next step, Bamford would like to see the project tested in space.
"I would like us to come up with some designs for making a test on a space craft or to piggy back on someone else's.
"I would like to have a small shield on a spacecraft to discover when we switch it on or off we can see the radiation radically reduce or disappear," she said.
In the meantime, private companies are pressing ahead with their Mars missions. Elon Musk, the CEO of SpaceX and Tesla Motors, is aiming for a manned mission in the mid-2020s.
NASA too has turned its attention to the problem, studying a shielding technique
using carbon, boron, nitrogen and hydrogen in tiny tubes.
"Some of the solutions are technology we have already, like hydrogen-rich materials, but some of it will necessarily be cutting edge concepts that we haven't even thought of yet," space radiation engineer Jonathan Pellish says on the NASA website
So let's assume we can find a way to keep our space explorers safe. How are we going to get them anywhere in a hurry?
One form of propulsion that has been suggested is an anti-matter drive.
It sounds like something from science fiction but the principle sounds simple enough. You mix matter with anti-matter, they annihilate each other and there's an enormous release of energy that could be harnessed.
As RAL astronomer and space scientist Barry Kellett puts it: "The engine is simple. The problem is getting the fuel."
The particle accelerator at the CERN complex in Switzerland can make anti-matter but only creates extremely small amounts. With current technology it estimates that it would take about a billion years to make a gram
... and at huge cost.
You can't store anti-matter in a can -- it would destroy the can -- so it would have to be captured and held in a magnetic field. Then you have to get it into space, and safely.
If those seemingly impossible barriers could be crossed then RAL scientist Bob Bingham estimates that a spacecraft might be able to reach half the speed of light.
"In other words, it would take eight years to get to the nearest star which is four light years away and then another four years for a signal to get back," he said.
The problem can be eased slightly by sending tiny robotic probes, which does away with the cost and complexity of looking after humans in space for considerable periods.
"If it costs $1billion for a robot camera why spend $100 billion to get someone to press the button for you?" said Kellett.
What other ways are there of powering a spaceship? Many have been proposed, including solar sails
and photon laser thrusters.
NASA is encouraging new technologies with its Innovative Advanced Concepts program.
One of those studies focuses on PuFF -- pulsed fission-fusion propulsion system
-- which NASA says aims to make a "radical improvement in our ability to explore destinations across the solar system and beyond."
If we can't go there ourselves, perhaps we can explore remotely from the comfort of home.
The Gaia space telescope, with its billion-pixel camera, is already helping with this. The mission's aim is to build a three-dimensional picture of our galaxy, measuring precise distances to a billion stars.
The European Space Agency (ESA) says Gaia has already mapped the precise position of 1,142 million stars
, hinting at "treasures to come."
The James Webb Space Telescope (JWST), a successor to Hubble, is due to launch in 2018. Instead of studying visible and ultraviolet light like Hubble, the JWST will work in the infra-red spectrum, allowing scientists to detect more distant targets.
Perhaps these telescopes and future missions will help to build a bigger and more detailed picture of the hundreds of exoplanets that have already been discovered by NASA's Kepler space telescope.
A NASA team has been investigating the possibilities of a future telescope they've called the Advanced Technology Large-Aperture Space Telescope (ATLAST)
that would be able to resolve stars in galaxies more than 10 million light-years away.
"One of the killer apps currently planned for ATLAST is the ability to detect signatures of life in the atmospheres of Earth-like planets in the solar neighborhood," said ATLAST study scientist Mark Clampin on the NASA website.
It is possible that we may one day be able to detect seasons on other worlds -- something Virgin Galactic CEO George Whitesides thought possible in an interview with CNN in 2013
"I think there's a very good chance that we're alive when we actually find another 'Earth' in another solar system -- how profound is that?"
It's a confidence shared by RAL's Bob Bingham. " I envisage that we will see the signs of life on an exoplanet very soon," he told CNN.
Impossible ....or is it?
Imagine going back in time and meeting the first Europeans who arrived in what is now the United States. How would you explain satellite TV to them?
We routinely watch video on our cell phones and can travel to the other side of the planet in 24 hours. Some of these things weren't possible even a few decades ago.
So what else that we consider impossible now might be feasible in years to come?
Is there a way to separate space and time to allow us to reach places instantaneously? Could we warp space time to make a short cut like the characters in the "Star Trek" series?
In 2014, CNN reported that NASA's Harold White had been working to develop a warp drive that will allow spacecraft to travel at speeds faster than light
More recently, and a century after Albert Einstein predicted gravitational waves, they were finally proved to exist
. Could they be harnessed in some way to allow cosmic travel?
The answers to all the things -- including time travel -- might be ones we can't even imagine right now.
Or perhaps the person who invents the time machine is you ... then you'll have some explaining to do.