Every spring, the melted snow fills the riverbeds, opening the way back home for the salmon after a life swimming in the oceans.

In Upstream, each player controls a bank of salmon swimming upstream to lay their eggs where they were born. During their journey, they will face hungry bears, fierce birds of prey, and patient fishermen, all of which they must avoid in order to survive. These are not the only hazards the salmon must face as each round of play the strength of the water flow will cause some pieces of the river to fall back, making it impossible for some fishes to make their way upstream.

The game is played in rounds, with each player spending five points among their salmon tokens in order to move them, either swimming or jumping across the hexagonal tiled river. At the end of each round, the lowermost pieces of the river are removed from the game, along with any salmon tokens standing on them, then three new tiles are added to the uppermost side of the river. The game ends when all salmon are either deceased or on the spawn point at the very end of the river. Players then score points, according to the number and order of arrival of their salmon. The player with most points wins.