Covenants: A covenant defines the relationship between two parties, for example a marriage covenant.
The Bible is a story of God's covenant journey with man. God made 5 different covenants with 5 different people. We live under the 'New Covenant' which was made by Jesus with God. It started with Jesus death on the cross, and will end with Jesus return. In the picture below, the cross (red) is on the timeline at 30AD, and the New Covenant period is the blue area that stretches into the future. Lets talk about each of those 5 covenants (with bible verses listed in brackets and italics).

Noah made a covenant with God (see Genesis 123) and the fact that we see a rainbow is a reminder of that covenant. The Noah arrow, you can see crosses into out timeline, but is not actually a part of the New Covenant. It stands separate and alone.
Abraham and David both made covenants with God (see Genesis 456 and 2 Kings 789). They are the building blocks of the New Covenant, and are absorbed into and continue on as part of the New Covenant. The first few verses of Matthew lists Jesus bloodline from both Abraham and David. Abraham is the father of faith - he brings faith into the New Covenant. David was a singer and king - he brings worship and government into the New Covenant.
Moses made a covenant with God (see Deuteronomy 123). It started simple, but then Moses made it complicated. It involved laws about economic, social and spiritual systems. Priests governed all theses things (so they were the policemen, lawyers, judges, teachers, tax collectors, doctors, social workers and spiritual ministers). God declared a limited time on this covenant, until he established a new and better covenant. So the timeline shows Moses covenant became useless at the cross, and then died in 70AD, when the temple at Jerusalem was destroyed. The temple was the seat of power for the priests and their laws and systems.