Recently, newly developed Vision-Language Models (VLMs), such as OpenAI's GPT-4o, have emerged, seemingly demonstrating advanced reasoning capabilities across text and image modalities. Yet, the depth of these advances in language-guided perception and abstract reasoning remains underexplored, and it is unclear whether these models can truly live up to their ambitious promises. To assess the progress and identify shortcomings, we enter the wonderland of Bongard problems, a set of classical visual reasoning puzzles that require human-like abilities of pattern recognition and abstract reasoning. While VLMs occasionally succeed in identifying discriminative concepts and solving some of the problems, they frequently falter, failing to understand and reason about visual concepts. Surprisingly, even elementary concepts that may seem trivial to humans, such as simple spirals, pose significant challenges. Moreover, even when asked to explicitly focus on and analyze these concepts, they continue to falter, suggesting not only a lack of understanding of these elementary visual concepts but also an inability to generalize to unseen concepts. These observations underscore the current limitations of VLMs, emphasize that a significant gap remains between human-like visual reasoning and machine cognition, and highlight the ongoing need for innovation in this area.