Potential. energy curves of 65 and 147 low-lying 52 states of PtH and PtH+ are respectively constructed using the multireference configuration interaction with singles, doubles, and Davidson's cluster corrections (MRCISD+Q), and the spin orbit coupling effects are considered through the state-interaction approach with relativistic effective core potential spin orbit operators. Spectroscopic constants fitted from these curves are reported and are compared with the available experimental or theoretical values. With the aid of the theoretical results including transition dipole moments, some experimentally reported electronic states and spectral bands of PtH are analyzed and reassigned. This work provides useful reference data for future experimental and theoretical studies of PtH and PtH+.