There are at least five ways that radioactive material can escape from a nuclear power station, beyond being removed by human action. All five depend by definition on a breach of every containment.
Four of these releases occurred at Fukushima.
The one that didn't occur at Fukushima was an explosion that takes out the reactor vessel itself - the Chernobyl phenomenon.
The four that occurred at Fukushima are:
Water leakage from the reactor vessel
When water-levels in the reactor vessel drop, exposing the fuel rods to the air, the fuel-rods melt down. The resulting corium damages the reactor vessel, leading to a breach of that vessel, and the leakage of cooling water carrying radioactive particles from the damaged and (partially) melted fuel-rods, from the reactor vessel. Further breaches in the rest of the containment (see below) results in the water entering the outside environment. The evidence is that this happened at Fukushima reactor 1: not a "major" breach by some standards - i.e. not enough for a major loss of corium - but bad enough to create a significant discharge of highly radioactive water. This may also have happened at reactors 2 and 3.
Vapour loss from the reactor vessel
When water-levels in the reactor vessel drop, exposing the fuel rods to the air and to steam, the reaction between the zirconium cladding of the fuel-rods, as they crack, and the steam and water, at high temperatures, produces hydrogen gas. If the venting of this hydrogen gas is done without injecting lots of nitrogen into the vessel first, then when the very hot hydrogen is vented, carrying out some steam vapour and radioactive materials from the damaged fuel rods, it explodes in the air, breaching the rest of the containment, and putting the radioactive materials into the outside air; this happened at Fukushima reactors 1 and 3. As @whoplisp points out, this can happen through unintentional venting, where the pressure inside the reactor vessel lifts the drywell head - the Brunswick phenomenon. (Subsequent venting at Fukushima has only happened after nitrogen injection)
Water loss from the coolant circuit
As you can see from the diagram in the answer from @Zassounotsukushi , there are pipes - the coolant circuit - between the reactor vessel and the rest of the reactor. Breaks in these pipes, and loss of containment from explosions (as above), can result in water loss from the coolant circuit; when the fuel rods have been damaged, this water carries radioactive material with it. This happened in reactors 1 and 2, and possibly reactor 3, at Fukushima.
Breach of containment in the fuel-storage pond
When water-levels in the fuel-storage pond drop, exposing the fuel rods to the air; and the containment building is breached, the fuel rods get damaged and hydrogen gets produced; as above, this can result in an explosion breaching all containment, and an atmospheric distribution of radioactive material; this happened at Fukushima reactor 4.
Fortunately, for most of the time of the release at Fukushima, the wind was blowing out to sea, resulting in the radioactive material mostly getting deposited in the Pacific Ocean rather than on land. Total estimates of the amount of material released vary hugely, and we may never know the actual values. Estimates vary between less than 1% of the radioactive isotopes present; and 50% of the Chernobyl release.