The segregation of the first division clubs from the other professional clubs may seem unfair since, in theory, a second-division club could in a given year actually be the best club.  While that cannot be proven in a league competition, there are opportunities for all the professional and amateur clubs to play each other during the season.  This is the goal of the Cup competition, a nation-wide single-elimination tournament that pits the top clubs against the lowly amateurs, occasionally producing unbelievable upsets.  It is a prime opportunity for the Davids in soccer to take on the Goliaths.

Typically, the Cup competition goes six to ten rounds, depending on the number of clubs included (this would mean 64 to several hundred clubs included).  Not all clubs are invited.  Typically, first division clubs that did not make any European competitions are invited.  The top half or some percentage of the remaining professional divisions are included, plus a spreading of successful amateur clubs to round out the numbers.

Cup games are interspersed throughout the season.  In Germany, there are league days and Cup days and they never mix.  In England, club schedules shift routinely in order to accommodate Cup games.

Traditionally, when professional clubs play amateur clubs, the amateur club gets to play at home.  It is a thrill for the hometown fans when this happens, although the professional clubs will often treat such games as a breather and play their second string.  Lower professional clubs will often host first division clubs for the same reason.

The prestige of the Cup final differs from country to country.  England's FA Cup is arguably the most prestigious, with the Final being a major event.  Meanwhile, the Cup competition in Germany gets almost no notice whatsoever, and some players view it as a nuisance that unnecessarily adds games to the schedule.  Of course, it's important to note that Cup games do not impact the league, so if a second division club wins the Cup it does not earn promotion.  It must win its place in the league separately.  

At the same time, there are two European-wide club competitions.

• National club champions (and select runners-up) qualify for the UEFA Champions League the next season.  The Champions League plays on Tuesdays and Wednesdays and operates in four phases -- a qualification tournament, a first phase regular season (32 clubs), a second phase regular season (16 clubs), then an 8-team single-elimination playoff.  The playoffs are done by playing two games and combining the aggregate scores to determine a winner.
• National runners-up qualify for the UEFA Cup which is a straight single-elimination tournament comprised of 128 clubs Europe wide.  UEFA Cup games are often played on Thursdays.  Two game playoffs are used in the later phases.