Tumor tissue is composed of various kinds of cancer cells in terms of genetic mutations and epigenetic alternations. This is called "heterogeneity" with the emerging concept of "cancer stem cells" or "tumor-initiating cells." The epigenetic change shows higher plasticity more than genetic mutations; I mean that epigenetics is dynamic, whereas genetics is static!  

Depending on cancer types, the degree of contribution of epigenetic change which would be reset by HDAC inhibitors is totally different. For example, malignant melanoma cells depend on JARID1B-induced epigenetic change to acquire malignant potential including metabolic reprogramming, invasive and metastatic phenotype. That is why not a few researchers insist that there is no cancer stem cells in melanoma.    

I strongly recommend you to read the following literature; J Cell Physiol. 2009 Sep;220(3):538-47. doi: 10.1002/jcp.21799. Genetic and epigenetic heterogeneity in cancer: a genome-centric perspective. Heng HH1, Bremer SW, Stevens JB, Ye KJ, Liu G, Ye CJ. 

Tumor tissue is composed of various kinds of cancer cells in terms of genetic mutations and epigenetic alternations. This is called "heterogeneity" with the emerging concept of "cancer stem cells" or "tumor-initiating cells." The epigenetic change shows higher plasticity more than genetic mutations; I mean that epigenetics is dynamic, whereas genetics is static!  

Depending on cancer types, the degree of contribution of epigenetic change which would be reset by HDAC inhibitors is totally different. For example, malignant melanoma cells depend on JARID1B-induced epigenetic change to acquire malignant potential including metabolic reprogramming, invasive and metastatic phenotype. That is why not a few researchers insist that there is no cancer stem cells in melanoma.    

I strongly recommend you to read the following literature; J Cell Physiol. 2009 Sep;220(3):538-47. doi: 10.1002/jcp.21799. Genetic and epigenetic heterogeneity in cancer: a genome-centric perspective. Heng HH1, Bremer SW, Stevens JB, Ye KJ, Liu G, Ye CJ. 

In my experience, one type of cancer does respond to one type HDACi treatment better than cancers, which means this type of cancer is more sensitive to this HDACi. And also, in the reality of clinical trials, many HDAC inhibitors are specialized in the treatment of one certain type of cancer. For example, SAHA has been proved by FDA to treat CTCL patients years ago, but the application in other solid tumors is still under investigation. Actually, the same goes with other epigenetic drugs. To answer this question, we have to understand that the epigenome of different tumors originated from different organs is quite different, although the genomic information they carry might not be much different. As in the case of HDAC inhibitors, acetylome, which is the target of HDAC inhibitors, varies between different tumors. So this makes things a lot easier to understand. For example, CTCL tumors may bear abnormal acetylome, which is sensitive to SAHA. Other in other tumors, the dysfunctional acetylome might be different and renders them less sensitive to SAHA treatment.

Anyway, I think this is common in cancer epigenetics. As a major contributor of cancer development, epigenetics has many different respects, ranging from DNA methylation to histone modification. Any anormaly or combination of many anormalies may lead to the rise of cancer, which demands relatively specific targeting for treatment.

Epigenetics is not a single phenomenon in that it does not affect a single gene and is the result of different mechanisms contributing to cancer specific epigenetic marks (DNA methylation, histone modifications, miRNAs). Probably, in various cancers, the pathways affected and the genes involved in those specific pathways are regulated by a certain class of HDACs making them sensitive to a specific HDACi treatment. Perhaps, it is not the HDAC itself but the downstream functions that it regulates or controls determines the effectiveness of the treatment. If all cancers exhibited the exact same epigenetic profile they could very well be treated by the same inhibitor and such is not the case.

In cancer lot of transcription factors, epigenetic modifiers etc. are involved. It depends on the factors involved the outcome of HDACi or any other treatment varies. 

Very nice question. First of all, the typical cancer pathway of different type of cancers that is called heterogeneity of cancers might be the perfect answer but yet to be clarified the mysterious events behind of heterogeneity and mutation on targeting moiety. In respect of epigenetics and HDAc inhibitors, a few type of cancers like CTCL, cervical cancer, lung cancer, T-cell lymphoma are benefited and many others cancers are under clinical trial. However, HDAcs are showing comparatively lower toxicities than other chemotherapeutics. It is the most important to deliver any anticancer drug into the cancer cell I mean inside the cancer cell rather than such type getting common phenomena of benefits and thereby controlling genotypes of the origin of that cancers. Around the year, billions of dollar are being invested behind the cancer research but you see the feedback very frustrating, one month in mice model, 6 month or a year or very hardly a little more in human models with combined so called cocktail therapy.

As mentioned above, HDACi are approved for certain leukemia and lymphoma diseases. In contrast to that, HDAC inhibitors have revealed some problems in solid tumors. In prostate cancer cells induction of EMT was observed. And selective inactivation of HDAC4 induced Tamoxifen-resistance in breast cancer cells via microRNAs (see references below).

Kong, D.; Ahmad, A.; Bao, B.; Li, Y.; Banerjee, S.; Sarkar, F.H. Histone deacetylase inhibitors induce epithelial-to-mesenchymal transition in prostate cancer cells. PLoS ONE, 2012, 7, e45045.

Ahmad, A.; Ginnebaugh, K.R.; Yin, S.; Bollig-Fischer, A.; Reddy, K.B.; Sarkar, F.H. Functional role of miR-10b in tamoxifen resistance of ER-positive breast cancer cells through down-regulation of HDAC4. BMC Cancer, 2015, 15, 540.