I shall discuss two monolayer transition metal dichalcogenides (TMD) that have unusual properties and are insulating for very different reasons.
TaSe2 is a cluster Mott insulator that is a promising candidate for a quantum spin liquid with spinon Fermi surface. I shall discuss the formation of a Kondo resonance between a magnetic impurity and the spinon Fermi surface and its consequence for STM tunneling. Monolayer WTe2 is a topological quantum spin Hall insulator. Recently sharp quantum oscillation peaks in the conductivity have been discovered in the insulator that resembles the quantum oscillations in metals. I shall show that modeling the system as an excitonic insulator can provide an explanation.