The Sevens are often stories of struggle with our desires, internally or externally. When faced with a Seven, we can be faced with doubt. This doubt, however, can also a path to knowledge. On the Tree of Life, Sevens are associated with the Sefirot Netzach, "Eternity/Victory/Enduring". This association is a little counter-intuitive as the situations described by the cards do not necessarily endure. The Sevens can be seen as partial success, and that which endures is oneself through the struggle rather than an enduring situation or achieving a desired result.
Mars in Leo
The Seven of Wands tells of a power that can make its way past obstacles and the odds stacked against it. It may be a little coarse, it may need refinement, but the raw strength to see an activity through is present.
Venus in Scorpio
The Seven of Cups is about discovering our fantasies, for better or worse. On the one hand we may be presented with the object of our desire, one that we yearn for from our deepest sense of longing. Coming close to this desire could bring deep satisfaction, if only for a moment. On the other hand, we may become entranced with that object, losing focus on what else is going on around us, and possibly missing something even more valuable while our attention is fixated elsewhere.
The Seven of Cups sometimes appears when we are presented with what seems to be more than one good option and a difficult decision must be made, or when we are not seeing something because our emotions are fixated on something that enthralls us. It can indicate that we momentarily get what we desire, but it will not last without completing the journey.
Moon in Aquarius
The Seven of Swords tells a tale of putting much effort into something (particularly into making plans or other "airy" or less physical activities) but not seeing the result one had hoped for. This is not necessarily negative, but could be unexpected.
Saturn in Taurus
The Seven of Disks is a similar situation to the Swords, except in a more physical manner--putting in effort but not seeing the fruits one expects or feels like one deserves. It is akin to a season's crop only partially coming to harvest, or planting beans and getting peas instead.