The exponential period conjecture predicts how the Galois group of an exponential motive governs all polynomial relations among its periods. For classical motives (which are special exponential motives) this conjecture specialises to the classical period conjecture. My aim is to present some elementary, yet elucidative examples of exponential motives and periods which illustrate how the exponential period conjecture implies certain popular transcendence conjectures, and how its non classical part is related to the Siegel-Shidlovskii theorem.[-]