Indeterminate forms arise in calculus when evaluating limits that do not lead to a clear value. Common examples include expressions like 0/0, ∞/∞, and ∞ - ∞. These forms indicate that further analysis is needed to determine the limit's actual value, as they can represent multiple outcomes. To resolve indeterminate forms, techniques such as L'Hôpital's Rule, algebraic manipulation, or Taylor series expansion are often employed. These methods help clarify the limit by transforming the expression into a determinate form, allowing for a precise evaluation of the limit as it approaches a specific value.