In this paper, we first provide a brief overview of Landau-type theorems for log-p-harmonic mappings. Next, we establish four new versions of Landau-type theorems for certain bounded p-harmonic mappings F with J(0) = 1 . Then, as applications of these results, the corresponding Landau-type theorems for certain log-p-harmonic mappings f with J(0) = 1 are provided. In particular, several sharp results of Landau-type theorems for certain bounded p-harmonic mappings or log-p-harmonic mappings with J(0) = 1 are obtained. Finally, we also establish a Landau-type theorem for a certain bounded log-p-harmonic mappings with J(0) = 1 , which improves the corresponding results of different authors.