The absence of significant commercial spaceflight in the early part of the twenty-first century - despite the predictions of writers and commentators throughout the twentieth century - is a continuing fact, the prodigious efforts of Elon Musk and others notwithstanding. The standard reasons are economic arguments; with a few counter-examples (such as Satellite Television), there are few advantages even to orbital spaceflight.
Of course, if getting into orbit was much cheaper, then the economics would quite definitely change. To achieve this objective, the current focus is on re-usable spacecraft: rather than have to burn up an expensively-engineered booster or capsule after a single launch, allow the craft itself to return to earth to be flown again.
There is also a trend towards the use of more easily handled fuels. Rather than the use of cryogenic hydrogen which made the old Saturn V launchers - the ones which put the Apollo astronauts on the Moon - quite so expensive and deadly, modern thinking is towards the use of fuels like kerosene - ordinary aircraft jet fuel - which is used safely every day.
Of course, the whole business remains very dangerous. You just have to remember the events of Apollo 13, or the catastrophe that was the Challenger explosion to realise that the fates of space missions and the astronauts they carry are still subject to sudden change, without notice.
So what is really required is a safe and energy-efficient way of getting from the surface of the earth to low orbit. Fortunately, such a solution was invented several decades ago; it's called the space elevator. Basically, a space elevator is a cable linking a fixed point on the earth to a satellite in geosynchronous orbit - so that, like orbital TV transponders, the satellite stays in the same relative position in the sky at all times. You can haul yourself up and down the cable using no more energy than a lift in a high building. Of course, the lift cages themselves would have to be suitably airtight and screened from radiation, but they wouldn't need any kind of rocket motors at all.
The trouble with space elevators is that they are more than a little tricky to make: the stresses on the cables would tear apart ordinary high-tensile steel in an instant. What is needed is some kind of super-strong material. Oh, and you need such exotic materials to be available, in space, in quantities measured in thousands of tonnes, since the elevator cables must be lowered from orbit. The organisational, logistic and engineering challenges involved in supplying such vast quantities of carefully extruded materials is quite beyond us at present; we'll probably have to strip-mine a few asteroids before we can even start of providing the raw materials for such an enterprise and we'll have to build a fairly sophisticated manufacturing capability in low orbit to deliver the heavily-processed outputs. All-in-all, quite a challenge, collectively, for the human race.