There are currently 3 obtainable fishing rod upgrades which are crafted using the previous tier and several items, these upgraded tiers increase attributes like the way bait can, but can be used in together with bait
Nature rod, this rod is caught from treasure chests it slightly increases attributes like fishing speed and chance for rarer fish, found also as an uncommon drop from treasure chests
Iron rod, created by reinforcing the nature rod with iron ingots, further increases speed and fish rarity modifier as well as adding a small chance for drops to be doubled
The crafting recipe for the Iron fishing rod, the Nature rod in the middle
Gold rod, created using the iron rod and two golden blocks, increases even more fishing speed and rarity modifier as well as having a reasonable chance for double drops
The crafting recipe for the Gold fishing rod
The Star fishing rod, is a mythical rod with an insane fishing speed and massive rarity modifier can only be caught as a legendary drop from treasure chests, so get fishing!