All known problems can be solved with algorithms. For all we know, humans are Turing machines.
Most problems can be structured into a graph. Graphs have vertices (entities holding data) and edges (from one vertex to another, sometimes with a value).
Many problems can be structured into a tree. Trees are connected graphs without cycles. Most trees we use are rooted: one vertex is the entry point (the root); it is the only vertex with no edge pointing to it, all other have exactly one. Many trees are ordered: vertices order their children like a list.
Some problems can be structured into a list. Lists are rooted trees where a maximum of one child is allowed.
A few problems can be structured into a map. Maps are directed graphs where every vertex has either a single edge coming from them (keys) or at least one edge coming from a key (values).
(An uncommon variation of maps are multimaps, where keys can have more than a single edge coming from them.)
Another structure is a set. Sets are graphs with no edges.