Interpretation v. Invalidation
Every modern Western style political system has courts or court-like institutions that interpret all legal pronouncements with legal force, including any sort of basic law or constitution, whether or not it is entrenched, and whether or not it is contained in a master document or spread across multiple enactments. Even the minimal norm that the courts should require everyone including the government to act lawfully that this generally implies, is not insignificant.
For example, even in the U.K., discussed below, or the Netherlands, discussed in the answer by JJJ, a judge in an ordinary trial court could resolve a conflict between an act of parliament and a local council ordinance, or could determine that a public official took an unlawful act that should not be given legal effect when determining the legal effect of the official's actions.
The question of judicial review is not whether courts have a role in interpreting foundational authoritative texts and norms, but if they can, in the extreme case, hold that is duly enacted law or government action is invalid or wrongful even if taken by the highest legislative or executive branch authority.
Also, in many countries, especially those with a civil law tradition, even in modern legal systems, not every judge can engage in judicial review of the constitutionality of a law or government action, only judges of a single, special constitutional court charged with that duty that is procedurally disengaged from the ordinary business of courts in interpreting the law. Prior to World War II, few countries with a civil law legal tradition recognized any power of judicial review, and even now, not all civil law countries (e.g. the Netherlands as noted in an answer from JJJ) grant the courts this power.
Only a minority of countries fuse constitutional interpretation of an entrenched supreme single constitutional document as fully with the ordinary business of judicial legal interpretation. In the U.S., any U.S. local, state, or federal judge can declare a law unconstitutional (contrary to popular belief, the U.S. does not reserve this power to the U.S. Supreme Court), but most countries don't allow this. The U.S. is also exceptional in that, unlike most judicial systems, many judges are elected and most judges who are not elected are political appointees, rather than civil servants in the usual sense selected based upon merit. This arguably gives the U.S. judiciary greater legitimacy to resolve the political questions found in many issues of constitutional law, than in countries where judges are (in theory and by means of appointment, at least) apolitical civil servants.
So, to some extent, the different means and scopes for enforcing political norms and protections for individual rights are just a difference of degree or personnel.
The Case Of British Parliamentary Supremacy
The United Kingdom is famous for having no truly entrenched laws (i.e. for having no statutes that cannot be overruled with an ordinary act of parliament) and for not having the laws governing the basics of its political organization and fundamental rights enshrined in a single document called a "constitution."
In that system, individual legislators have recognized a heightened, almost quasi-judicial, obligation to respect democratic political norms and to honor human rights, since legislative overreaching is not easily corrected by the courts. When the system is working properly, elected officials feel a sense of responsibility to the system as well as to their constituents and their partisan causes and recognize that while ordinary political issues are partisan, that a handful of core political norms call for legislators to put process and decency, over policy and partisanship.
In a system without judicial review, legislators know that there is no "safety net" in the courts to undo their actions if they act irresponsibly, so the real world cost of crossing the line of political or human rights norms has greater stakes. In contrast, in countries with strong judicial review, legislators can pass legislation for partisan purposes that offend these norms, knowing that this is just theater that is morally acceptable because the laws that they vote for will be overturned later by the courts.
Notably, in the handful of years under the current United States Constitution adopted in 1789, and before Marbury v Madison was decided by the U.S. Supreme Court, President George Washington felt such an obligation when exercising his veto power.
This was supplemented in the post-World War II era by treaties, most notably those associated with the Council of Europe, which is primarily an international organization that seeks to get European countries to commit by treaty to protections for individual human rights, and by treaties associated with the European Union and its various related European free trade arrangements.
While the U.K. parliament, in theory, can abrogate a treaty even when the treaty on its face provides no means for exiting from the treaty, there is a strong political norm towards not leaving a treaty except by the means set forth in the treaty.
Leaving a treaty otherwise could be subject to international sanctions. Politically, formally taking the steps to abrogate a human rights treaty could have electoral costs for the political parties and individual members of parliament backing that move. Even leaving the European Union in Brexit, according to the procedures in the E.U. treaties was highly politically controversial, over something far less fundamental than intentionally abrogating human rights.
It also helps in such a system to have an electorate who is acculturated politically over generations to share core values about the democratic political process and human rights that the public cares enough about to hold its electoral officials accountable for, if those officials take steps to abrogate those norms.
Judicial Review v. Parliamentary Supremacy
This seems very different from the system in countries that have judicial review of legislation and government actions for constitutionality by some court or courts with the authority to do so.
But ultimately, somewhere down the line, upholding a political norm or human rights norm embedded in some legal enactment or shared understanding is something that some group of senior political actors, be they judges or legislators or executive branch officials, or military officers, must do.
Ideas and laws written in books don't spontaneously implement themselves. Some person in a position of power has to draw the line.
In a system with judicial review, judges take on the role of caring about process and human rights more than partisan priorities, and legislators are free to act with less regard for these higher principles. In a system with parliamentary supremacy, courts have to wear both hats.
Viewing this as a matter of processes and political roles in a legal system, rather than viewing judicial review as an indispensable institution, is appropriate. This is because, in the Western political tradition, countries that lack this political institution have not necessarily been more unjust, tyrannical, and undemocratic, and countries with this political institutions, have not necessarily been above reproach in their respect for democratic values and human rights. The institution of judicial review is often critical in an overall political system which has developed a political culture that heavily relies upon this institution, but its importance is not necessarily universal across all political cultures.
For example, the Netherlands and the U.K., which have entirely or mostly lacked judicial review of legislation by courts, have not historically been particularly egregious in their lack of respect for democracy and human rights.
East Asian Political Theory Compared
In East Asian political theory rooted in Confucianism, the debate over how to prevent the government and people in authority from doing unjust things focused on trying to choose leaders who were trained in moral analysis through the study of the Confucian classics and examinations on their application, and by choosing good men (it was almost always men back then) rather than having a "rule of law" which was viewed as something inherently subject to manipulation by perfidious lawyers with questionable motives.
The notion was that "there is always sky above the sky", i.e. that everyone but the Emperor of the entire nation himself, always has someone above them to whom they must submit if they get out of line.
The best that society could do in the final step of the Emperor himself, was to train the Emperor to act justly with training from the Confucian classics, to have an Emperor who literally owned everything and everyone and like a property owner had a personal interest in making what he owned (everything and everyone in his Empire) as valuable as possible, and who as a hereditary monarch did not have to attain his position out of narcissistic ambition. Society had to trust that this one person out of everyone in the country, the Emperor, did indeed, as claimed, benefit from divine guidance or was a god himself.
In much the same way, in the U.S., the people and the system has to trust that the U.S. Supreme Court with its final say on the legality of government actions and laws, will do the right thing, as a result of their careful means of selection and long training in making these decisions.
In both the cases of the Emperor, and in the case of the U.S. Supreme Court, in reality, the results are not alway perfect.