The more or less obvious "absolute" contraindications for liver transplantation, in the presence of which liver transplantation is not discussed, include the following circumstances:

Severe decompensated pathology of the cardiovascular system or lungs
Continuing dependence on alcohol or drugs
Hepatocellular carcinoma with metastatic extension
Active infectious processes that are not amenable to therapy (bacterial endocarditis without success from therapy, AIDS, active tuberculosis with the impossibility of cure, etc)
Anatomical abnormalities that technically do not allow liver transplantation
Intrahepatic cholangiocarcinoma
Hemangiosarcoma
Systematic compliance

Before upcoming liver transplantation, patient undergoes the following examinations and procedures:

anthropometric measurements (height, body weight, abdominal circumference, etc.);
analysis for blood group and Rh factor;
coagulogram;
blood tests for HIV, HCV-Ab, syphilis, HBcor IgG and HBcor IgM, HBs-Ag, HBe-Ag, HBe-Ag;
blood test for PCR (when detecting diseases of HCV or HBV);
bacteriological cultures of discharge from the nose and throat, sputum, urine, feces and vaginal discharge;
study of the function of external respiration;
chest x-ray;
esophagogastroduodenoscopy;
ECG 
ultrasound of the abdominal organs with obligatory Doppler examination of the vessels of the liver and kidneys;
colonoscopy;
radioisotope study of the kidneys;
static and dynamic kidney scintigraphy;
HLA (tissue typing);
blood tests for tumor markers: CEA, AFP, Ca-19-9;
direct or indirect cholangiography;
MRI cholangiography (if necessary);
CT of the chest and abdomen with contrast (if tumor is suspected);
puncture biopsy of the liver (if necessary);
analysis of ascitic fluid (during laparocentesis);
diagnosis of fermentopathies, autoimmune diseases and other specific tests, depending on the clinical case;
dentist consultation;
consultation with an anesthesiologist;
a council of doctors of transplant center.

When identifying indications and excluding contraindications for liver transplantation with patients included in the waiting list, the following work is carried out:

Determination and correction of nutritional status.
Continuous dynamic monitoring of esophageal varices and their endoscopic ligation (as needed).
Vaccination of patients against hepatitis B, who have not identified markers of HBV infection.
Decompression and sanitation of the biliary tract.
Psychotherapeutic preparation of patient for upcoming transplant.

Sometimes the following complications develop after liver transplantation:

bleeding - occurs in about 7.5% of cases;
vascular complications (steal syndrome, thrombosis, narrowing of the hepatic artery) - such consequences are very dangerous and require repeated transplantation, occur in about 3.5% of patients;
primary inactivity of the transplanted liver - this complication occurs infrequently, but also requires re-transplantation;
obstruction of hepatic veins - rarely occurs, is more often observed with transplantation of a part of the liver;
stenosis or thrombosis of the portal vein - detected by ultrasound in approximately 1.3% of patients and, if immediate treatment is carried out, can be eliminated without surgery;
immunological problems - in many patients, acute or chronic rejection of the transplanted organ may occur, in acute cases, the necessary measures may be taken to stop this process, but it is very difficult to fight chronic rejection;
small graft size syndrome - occurs only with liver transplants from a living donor, when surgeons have incorrectly calculated the size of the transplanted organ part (if the signs of such a syndrome do not go away after two days, then there is a need for a second operation);
infection - in many patients it can be asymptomatic, but in others it leads to severe inflammatory processes and can become the cause of death (to prevent such a complication, patient is prescribed antibiotic therapy before the operation);
bile leakage and biliary structures - occur quite often in patients of any age.