Abstract: Despite their remarkable achievements, modern Large Language Models (LLMs) encounter exorbitant computational and memory footprints. Recently, several works have shown significant success in *training-free* and *data-free* compression (pruning and quantization) of LLMs achieving 50-60\% sparsity and reducing the bit-width down to 3 or 4 bits per weight, with negligible perplexity degradation over the uncompressed baseline. As recent research efforts are focused on developing increasingly sophisticated compression methods, our work takes a step back, and re-evaluates the effectiveness of existing SoTA compression methods, which rely on a fairly simple and widely questioned metric, perplexity (even for dense LLMs). We introduce **K**nowledge-**I**ntensive **C**ompressed LLM Benchmar**K** **(LLM-KICK)**, a collection of carefully-curated tasks to re-define the evaluation protocol for compressed LLMs, which have significant alignment with their dense counterparts, and perplexity fail to capture subtle change in their true capabilities. LLM-KICK unveils many favorable merits and unfortunate plights of current SoTA compression methods: all pruning methods suffer significant performance degradation, sometimes at trivial sparsity ratios (*e.g.*, 25-30\%), and fail for N:M sparsity on knowledge-intensive tasks; current quantization methods are more successful than pruning; yet, pruned LLMs even at $\geq 50$\% sparsity are robust in-context retrieval and summarization systems; among others. LLM-KICK is designed to holistically access compressed LLMs' ability for language understanding, reasoning, generation, in-context retrieval, in-context summarization, *etc.* We hope our study can foster the development of better LLM compression methods. The reproduced codes are available at https://github.com/VITA-Group/llm-kick.